austms 2018 - maths.adelaide.edu.au

AustMS 201862nd Annual Meeting of the Australian Mathematical Society

4-7 December, University of Adelaide

Program and Abstracts

The abstracts of the talks in this handbook were provided individually by the authors. Only minortypographical changes have been made by the editors. The opinions, findings, conclusions and recom-mendations in this book are those of the individual authors.

Editors: Thomas Leistner, Guo Chuan Thiang and Hayden Tronnolone

Cover Design: Andrew Black

Template and Registration System: John Banks

Conference Website: maths.adelaide.edu.au/austms2018

http://maths.adelaide.edu.au/austms2018/

ContentsForeword 3

Conference Organisation 4

Conference Sponsors 5

Conference Program 6

Program by DayTue 4 December 2018 9Wed 5 December 2018 14Thu 6 December 2018 19Fri 7 December 2018 23

Session 1: Plenary Lectures in the The Braggs Lecture Theatre 27

Special Sessions2. Algebra 283. Applied and Industrial Mathematics 304. Category Theory 315. Computational Mathematics 326. Differential Geometry 337. Dynamical Systems and Ergodic Theory 348. Functional Analysis, Operator Algebra, Non-commutative Geometry 359. Geometric Analysis 37

10. Geometry and Topology 3811. Harmonic Analysis 3912. Integrable Systems 4013. Mathematical Biology 4114. Mathematics Education 4215. Mathematical Physics 4316. Number Theory 4417. Optimisation 4518. Probability Theory and Stochastic Processes 4719. Representation Theory 49

Plenary Abstracts 51

Special Session Abstracts 512. Algebra 563. Applied and Industrial Mathematics 604. Category Theory 645. Computational Mathematics 666. Differential Geometry 697. Dynamical Systems and Ergodic Theory 728. Functional Analysis, Operator Algebra, Non-commutative Geometry 749. Geometric Analysis 78

10. Geometry and Topology 8011. Harmonic Analysis 8312. Integrable Systems 8513. Mathematical Biology 8714. Mathematics Education 8915. Mathematical Physics 9316. Number Theory 9517. Optimisation 9718. Probability Theory and Stochastic Processes 102

19. Representation Theory 106

List of Registrants 111

Index of Speakers 117

Conference Timetable 119

2

Foreword

It is a pleasure and an honour to welcome the participants of the 62nd Annual Meeting of the AustralianMathematical Society to the University of Adelaide. I hope you will find the scientific program of theconference inspiring and that you will enjoy the associated events we have organised.The program of the conference comprises 13 plenary lectures by internationally renowned mathemati-cians from four continents and all areas of mathematics. The plenary lectures will feature talks byHanna Neumann Lecturer Hinke Osinga, Early Career Lecturer Renato Ghini Bettiol and ANZIAMLecturer Steven Sherwood.The conference is accompanied by several associated events, starting with the Early Career Workshopon the weekend before the conference. There will be a public lecture on the mathematical problemsrelated to determining the precise shape of the earth. This public lecture will be given by Etienne Ghys,who recently gave a public lecture to Brazilian high school students at the ICM in Rio de Janeiro. TheAustMS meeting will also feature an Education Afternoon aimed at high school teachers. Continuing atradition that started at last year’s conference, Lewis Mitchell has organised a debate on the questionwhether or not mathematics is better done by computers than by humans. I am very curious to seehow both debating teams will argue their case.In addition to the scientific program, there will be several social events, starting with the Women inMathematical Sciences Dinner on the evening before the conference, a Welcome Reception and theConference Dinner at the National Wine Centre of Australia. The latter brings me to a vital aspect ofthe conference program: the student talks and the Bernhard H. Neumann Prize. This year there willbe 68 talks by students; the B. H. Neumann Prize Committee chaired by Masoud Kamgarpour willwork tirelessly during the first three days of the conference to find the best talk and to award the prizeat the conference dinner.At the heart of the Annual Meeting are the special sessions. Here we will see a cross section of thebeautiful and useful mathematics that is created in Australia. I would like to thank all the sessionorganisers who put together the 18 special sessions, some of which have such a striking variety of talksthat they almost exceed the limitations of a four day conference.Finally, I want to thank everyone who helped to organise this conference, including some who arenot mentioned explicitly as helpers on the next page. First of all I would like to thank the studentvolunteers who helped to pack the conference bags and staff the registration table. Further thanksgo to the Society’s outgoing and incoming Vice Presidents Annual Conferences Vladimir Gaitsgoryand Vladimir Ejov and the Secretary Peter Stacey for providing me with initial directions, as well asto the members of the Program Committee for putting together an excellent list of plenary speakers.Special thanks goes John Banks, who never got tired of answering my questions about his fabulousRegister! and adjusting it to the needs of this conference. I would also like to thank Yvonnes Stokes,the Chair of the WIMISG Executive Committee, who helped to organise the Women in MathematicsDinner and was unfortunate enough to have her office just a few doors down from mine, so that Icould spontaneously ask for her advice on important aspects of the conference. I also thank the localorganising committee and the context of this foreword allows me to single out two of them, Guo ChuanThiang and Hayden Tronnolone, who worked tirelessly to bring this conference booklet into a form thatwe could confidently put into the conference bags. Even with help from so many sides, this conferencewould not have been possible without the administrative support that was provided by the Facultyof Engineering, Computer and Mathematical Sciences, in particular the help of Madelaine Veltmanwho kept a close eye on the essential details of such a large event, including those which conferencedirectors tend to forget or ignore.I hope you all enjoy the conference as much as I enjoyed the challenge of organising it and I wish youa wonderful and memorable week in Adelaide.

Thomas Leistner

Conference Director

3

Conference Organisation

Program Committee

Ben Burton (University of Queensland)Alan Carey (Australian National University)Julie Clutterbuck (Monash University)Alice Devillers (University of Western Australia)Peter Forrester (University of Melbourne)Gary Froyland (University of New South Wales)Vladimir Gaitsgory (Macquarie University)Thomas Leistner (University of Adelaide)Giang Nguyen (University of Adelaide)Jacqui Ramagge (University of Sydney)Lesley Ward (University of South Australia)

Local Organising Committee at the University of Adelaide

Thomas Leistner – Director

Sanjeeva Balasuriya – Special SessionsDavid Baraglia – Special SessionsAndrew Black – Conference Poster and Booklet Cover DesignJudith Bunder – Women in Mathematical Sciences DinnerBarry Cox – TreasurerPeter Hochs – SecretaryMelissa Humphries – Women in Mathematical Sciences DinnerLewis Mitchell – DebateGiang Nguyen – SponsorshipDavid Roberts – VolunteersYvonne Stokes – Women in Mathematical Sciences DinnerGuo Chuan Thiang – BookletHayden Tronnolone – Booklet and WebsiteRaymond Vozzo – Education Afternoon

Allison Dinan – Administrative supportSharyn Liersch – Administrative supportMadelaine Veltman – Administrative support

Registration System

John Banks (University of Melbourne)

Early Career Workshop

Luke Bennetts (University of Adelaide)Michael Coons (University of Newcastle)Madelaine Veltman (University of Adelaide, administrative support)

4

Conference Sponsors

University of Adelaide

AustMS

AMSI

ACEMS

MATRIX

5

Conference Program

Overview of the Academic Program

The academic program comprises 248 talks, spread over 18 special sessions and including 13 plenarylectures and a public lecture. There are 68 talks presented by students and the names of studentspeakers are marked with a superscript “s”. For a short overview of the conference program, pleaserefer to page 119.

Tue 4 December 2018 – page 9Wed 5 December 2018 – page 14Thu 6 December 2018 – page 19Fri 7 December 2018 – page 23

B Overview Conference Timetable – page 119

Plenary Lecturers

Renato Ghini Bettiol – Early Career Lecturer (City University of New York, USA)Regina Burachik (University of South Australia, Australia)Josef Dick (University of New South Wales, Australia)

Etienne Ghys (Ecole normale superieure de Lyon, France)Manjunath Krishnapur (Indian Institute of Science, India)Joan Licata (Australian National University, Australia)Malwina Luczak (University of Melbourne, Australia)Hinke Osinga – Hanna Neumann Lecturer (University of Auckland, New Zealand)Nageswari Shanmugalingam (University of Cincinnati, USA)Steven Sherwood – ANZIAM Lecturer (University of New South Wales, Australia)Natalie Thamwattana (University of Newcastle, Australia)Geordie Williamson (University of Sydney, Australia)

B Timetable of Plenary Lectures – page 27

Special Sessions

1. Plenary – page 532. Algebra – page 563. Applied and Industrial Mathematics – page 604. Category Theory – page 645. Computational Mathematics – page 666. Differential Geometry – page 697. Dynamical Systems and Ergodic Theory – page 728. Functional Analysis, Operator Algebra, Non-commutative Geometry – page 749. Geometric Analysis – page 78

10. Geometry and Topology – page 8011. Harmonic Analysis – page 8312. Integrable Systems – page 8513. Mathematical Biology – page 8714. Mathematics Education – page 8915. Mathematical Physics – page 9316. Number Theory – page 9517. Optimisation – page 9718. Probability Theory and Stochastic Processes – page 10219. Representation Theory – page 106

6

Conference Program

Education Afternoon

The Education Afternoon will consist of talks by mathematicians aimed at school teachers describingsome interesting and cutting edge mathematical research and applications. The list of speakers andtalks is given below. The session will also feature information about the ChooseMaths programme,which is run by the Australian Mathematical Sciences Institute and is aimed at encouraging younggirls to continue their studies in mathematics.

I 15:00, Wednesday, 5th DecemberEducation Afternoon Tea and Education AfternoonHorace Lamb 422 (access via Hub Central)

Etienne Ghys (Ecole normale superieure de Lyon)The mathematics of traffic jams

Hinke Osinga (University of Auckland)Chaos and a pancake

Lewis Mitchell (University of Adelaide)Using mathematics to study online social networks

Social Program

I 18:15 Monday, 3rd DecemberWomen in Mathematical Sciences DinnerThe Playford, 120 North Tce, Adelaide

I 18:00 Tuesday, 4th DecemberWelcome ReceptionAtrium of the Ingkarni Wardli Building

I 18:00 Wednesday, 5th DecemberPublic Lecture ReceptionAtrium of the Ingkarni Wardli Building

I 19:00 Wednesday, 5th DecemberPublic Lecture by Etienne Ghys: The shape of our planet Earth: a mathematical challenge!The Braggs Lecture Theatre

I 19:00 Thursday, 6th DecemberConference DinnerThe National Wine Centre of Australia, Corner of Botanic & Hackney Roads Adelaide

Annual General Meeting of the Women in Mathematics Special Interest Group

I 17:00 Monday, 3rd DecemberWIMSIG Annual General MeetingH6-03 Level 6 of the Hawke Building, City West Campus, University of South Australia,55 North Tce, Adelaide

Annual General Meeting of the Australian Mathematical Society

I 14:00 Thursday, 6th DecemberAnnual General MeetingHorace Lamb Lecture Theatre

Lunch, Tea and Coffee

Throughout the conference, light lunches, tea and coffee will be served during the lunch breaks and themorning and afternoon teas in the Atrium of the Ingkarni Wardli Building (for times see the program).

7

Conference Program

Conference Information Desk

The information desk for the conference is located in the Ingkarni Wardli Atrium.

Publisher’s Display

Cambridge University Press will have a stall in the Ingkarni Wardli Atrium presenting publications ofthe Australian Mathematical Society.

Wireless Network Access

Eduroam is available on campus. Those who do not have access to Eduroam through their homeinstitution may use the network UofA Guest. The password is biscuitchef.

Security

The Security office is being temporarily relocated from the Kenneth Wills Building to Ground Floor ofthe Oliphant Building. The phone number is (08) 8313 5990.

8

Tue 4 December 2018

� Registration – Ingkarni Wardli Atrium 08:00 – 09:00

� Opening Ceremony and Awards – The Braggs Lecture Theatre 09:00 – 10:30

� Morning Tea – Ingkarni Wardli Atrium 10:30 – 11:00

� Plenary Lecture – The Braggs Lecture Theatre

11:00 I Geordie Williamson (The University of Sydney)

Semi-simplicity in representation theory


12:00 I Malwina Luczak (The University of Melbourne)

Near-criticality in mathematical models of epidemics

� Lunch – Ingkarni Wardli Atrium 13:00 – 14:00

� Afternoon Tea – Ingkarni Wardli Atrium 15:00 – 15:30


17:00 I Steven Sherwood (University of New South Wales)

Recent Advances in Climate Sensitivity

� Welcome Reception – Ingkarni Wardli Atrium 18:00 – 20:00

� Afternoon Special Sessions

2. Algebra

Horace Lamb Lecture Theatre

14:00 Jeremy Sumner (University of Tasmania)Markov association schemes (p. 58)

14:30 Alejandra Garrido (The University of Newcastle)Hausdorff dimension and normal subgroups of free-like pro-p groups (p. 57)

15:30 Timothy Peter Bywaterss (The University of Sydney)Spaces at infinity for hyperbolic totally disconnected locally compact groups (p. 56)

16:00 Carlisle King (The University of Western Australia)Finite simple images of finitely presented groups (p. 58)

16:30 Stephan Tornier (The University of Newcastle)Totally disconnected, locally compact groups from transcendental field extensions (p.59)

9

Tue 4 December 2018

3. Applied and Industrial Mathematics

Ligertwood 316

14:00 Andrei Ermakovs (University of Southern Queensland)Mathematical problems of long wave transformation in a coastal zone with a variablebathymetry (p. 60)

14:30 Ajini Galapitages (University of South Australia)Optimal scheduling of trains using connected driver advice system (p. 60)

15:30 Mark Joseph McGuinness (Victoria University of Wellington)MMM, microwaves measure moisture (p. 61)

16:00 Yvonne Stokes (The University of Adelaide)A coupled flow and temperature model for fibre drawing (p. 62)

16:30 Sevvandi Priyanvada Kandanaarachchi (Monash University)About outlier detection (p. 61)

4. Category Theory

Engineering and Mathematics EMG06

14:00 Yuki Maeharas (Macquarie University)Inner horns for 2-quasi-categories (p. 64)

14:30 Michelle Strumilas (The University of Melbourne)Infinity Cyclic Operads (p. 64)

15:30 Danny Stevenson (The University of Adelaide)The right cancellation property of the class of inner anodyne maps (p. 64)

5. Computational Mathematics

Ligertwood 314 Flinders Room

14:30 Garry Newsam (The University of Adelaide)A review of some approximation schemes used in FFTs on non-uniform grids (p. 67)

15:30 Robert Womersley (University of New South Wales)Using spherical t-designs and `q minimization for recovery of sparse signals on thesphere (p. 68)

16:00 Yuguang Wang (University of New South Wales)Sparse Isotropic Regularization for Spherical Harmonic Representations of RandomFields on the Sphere (p. 68)

16:30 Janosch Rieger (Monash University)Integrating semilinear parabolic differential inclusions with one-sided Lipschitznonlinearities (p. 67)

6. Differential Geometry

Barr Smith South 2051

14:00 Renato Ghini Bettiol (City University of New York)Convex Algebraic Geometry of Curvature Operators (p. 69)

14:30 Romina Melisa Arroyo (University of Queensland)The Alekseevskii conjecture: Overview and open questions (p. 69)

15:30 Ramiro Augusto Lafuente (The University of Queensland)Homogeneous Einstein manifolds via a cohomogeneity-one approach (p. 70)

16:00 Owen Dearricott (The University of Melbourne)Positive curvature in dimension 7 (p. 69)

16:30 Kelli Francis-Staites (The University of Oxford)Corners in C∞-Algebraic Geometry (p. 70)

10

Tue 4 December 2018

8. Functional Analysis, Operator Algebra, Non-commutative Geometry

Engineering South S111

14:00 Mathai Varghese (The University of Adelaide)The magnetic spectral gap-labelling conjecture and some recent progess (p. 77)

15:30 Jessica Murphys (The University of Sydney)C*-algebras associated to graphs of groups (p. 77)

16:00 Becky Armstrongs (The University of Sydney)A twisted tale of topological k-graph C*-algebras (p. 74)

16:30 Raveen Daminda de Silvas (University of New South Wales)Maximum Generalised Roundness of Random Graphs (p. 75)

9. Geometric Analysis


14:00 Miles Simon (Magdeburg University)Some integral estimates for Ricci flow in four dimensions (p. 79)

14:30 Ahnaf Tajwar Tahabubs (The University of Adelaide)Reduced SU(2) Seiberg-Witten Equations compared to SU(2) Ginzburg-Landauequations (p. 79)

15:30 Brett Parker (Monash University)Regularity of the dbar equation in degenerating families (p. 79)

16:00 David Hartley (University of Wollongong)On the Existence of Stable Unduloids of Dimension Eight (p. 78)

10. Geometry and Topology


14:00 Brett Parker (Monash University)Tropical geometry, the topological vertex, and Gromov-Witten invariants of Calabi-Yau3-folds, (p. 81)

15:30 Benjamin Burton (University of Queensland)Knot tabulation: a software odyssey (p. 80)

16:00 Anne Thomas (The University of Sydney)Commensurability classification of certain right-angled Coxeter groups (p. 82)

16:30 Daniel Francis Mansfield (University of New South Wales)Perpendicularity in Ancient Babylon (p. 81)

11. Harmonic Analysis

Ligertwood 111

14:30 Xuan Duong (Macquarie University)BMO spaces associated to operators on non-doubling manifolds with ends (p. 83)

15:30 Neil Kristofer Dizons (The University of Newcastle)Optimisation in the Construction of Symmetric and Cardinal Wavelets on the Line (p.83)

16:00 Hong Chuong Doans (Macquarie University)Maximal operators with generalised Gaussian bounds on non-doubling Riemannianmanifolds with low dimension (p. 83)

16:30 Xing Cheng (Monash University)Scattering of the nonlinear Klein-Gordon equations (p. 83)

12. Integrable Systems

Ligertwood 112

14:00 Nalini Joshi (The University of Sydney)Hidden solutions of discrete systems (p. 85)

14:30 Remy Alexander Addertons (The Australian National University)A generalized Temperley-Lieb algebra in the chiral Potts model (p. 85)

11

Tue 4 December 2018

15:30 Yibing Shens (The University of Queensland)Ground-state energies of the open and closed p+ ip-pairing models from the BetheAnsatz (p. 85)

16:00 Reinout Quispel (La Trobe University)Finding rational integrals of rational discrete maps (p. 85)

16:30 Kenji Kajiwara (Kyushu University)A new framework and extensions of log-aesthetic curves in industrial design byintegrable geometry (p. 85)

13. Mathematical Biology

Ligertwood 216 Sarawak Room

15:30 Jeremy Sumner (University of Tasmania)Predicating saturation in models of genome rearrangement in polynomial time (p. 88)

16:00 Yoong Kuan Gohs (University of Technology, Sydney)Pattern Avoidance in Genomics (p. 87)

16:30 Maria Kleshninas (The University of Queensland)Learning advantages in evolutionary games (p. 87)

14. Mathematics Education

Horace Lamb 422 (via Hub Central)

14:00 David Hartley (University of Wollongong)Student learning and feedback in higher education mathematics (p. 90)

14:30 Carolyn Kennett (Macquarie University)Mathematics and Indigenous Culture (p. 90)

15:30 Margaret Marshman (University of the Sunshine Coast)Making mathematics teachers: Beliefs about mathematics and mathematics teachingand learning held by academics who teach future teachers (p. 91)

16:00 Roland Dodd (Central Queensland University)First year engineering mathematics diagnostic testing (p. 89)

16:30 William Guo (Central Queensland University)You can teach old dogs new tricks if you know them well (p. 89)

15. Mathematical Physics

Engineering North N132

14:00 Anupam Chaudhuris (Monash University)One-point recursions of Harer-Zagier type (p. 93)

14:30 Arnaud Brothier (UNSW Sydney)Constructions of 1+1-dimensional lattice-gauge theories and the Thompson group (p.93)

15:30 Philip Broadbridge (La Trobe University)The conditionally integrable diffusion equation with nonlinear diffusivity 1/u (p. 93)

16:00 Iwan Jensen (Flinders University)Self-avoiding walks with restricted end-points (p. 94)

16:30 Anthony Mays (The University of Melbourne)Determinantal polynomials, vortices and random matrices: an exercise in experimentalmathematical physics (p. 94)

16. Number Theory

Ingkarni Wardli B17

14:00 Ole Warnaar (The University of Queensland)On modular Nekrasov–Okounkov formulas (p. 96)

15:30 Florian Breuer (The University of Newcastle)Heights and isogenies of Drinfeld modules (p. 95)

12

Tue 4 December 2018

16:00 Matteo Bordignons (University of New South Wales Canberra)Explicit bounds on exceptional zeroes of Dirichlet L-functions (p. 95)

16:30 Michaela Cully-Hugills (University of New South Wales Canberra)Square-free numbers in short intervals (p. 95)

17. Optimisation


14:00 Marco Antonio Lopez Cerda (Alicante University)A crash course on stability in linear optimization (p. 99)

15:30 Helmut Maurer (University of Mnster)Multi-objective Optimal Control Problems in Biomedical Engineering (p. 99)

16:00 Sabine Pickenhain (Brandenburg Technical University Cottbus)Optimal Control on Unbounded Intervals - Fourier-Laguerre Analysis of the Problem(p. 100)

16:30 Vladimir Gaitsgory (Macquarie University)On continuity/discontinuity of the optimal value of a long-run average optimal controlproblem depending on a parameter (p. 98)

18. Probability Theory and Stochastic Processes

Ingkarni Wardli B18

14:00 Kais Hamza (Monash University)Directed walk on a randomly oriented lattice (p. 103)

14:30 Kihun Nam (Monash University)Correlated time-changed Levy processes (p. 104)

15:30 Kostya Borovkov (The University of Melbourne)The asymptotics of the large deviation probabilities in the multivariate boundarycrossing problem (p. 102)

16:00 Andrea Collevecchio (Monash University)Branching ruin number (p. 103)

16:30 Lachlan James Bridgess (The University of Adelaide)Markov-modulated random walk search strategies for animal foraging (p. 102)

19. Representation Theory


14:00 Masoud Kamgarpour (University of Queensland)Topology of representation stacks (p. 107)

14:30 Iva Halacheva (The University of Melbourne)Puzzles for restricting Schubert classes to the symplectic Grassmannian (p. 107)

15:30 Alexander Ferdinand Kerschls (The University of Sydney)Inner products on graded Specht modules (p. 107)

16:00 Marvin Kringss (RWTH Aachen University)The p-Part of the Order of an Almost Simple Group of Lie Type (p. 108)

16:30 Seamus Albions (The University of Queensland)The Selberg integral and Macdonald polynomials (p. 106)

13

Wed 5 December 2018

� Award Talk – The Braggs Lecture Theatre 09:00 – 09:30


09:30 I Natalie Thamwattana (The University of Newcastle)

A mathematical journey into nanoscience and nanotechnology



11:00 I Manjunath Krishnapur (Indian Institute of Science Bangalore)

Nodal sets of eigenfunctions of the Laplacian, with randomness


12:00 I Joan Licata (Australian National University)

Just Enough Twisting


� Debate – The Braggs Lecture Theatre 14:00 – 15:00


� Education Afternoon Tea – Horace Lamb 422 (via Hub Central) 15:00 – 15:30

� Education Afternoon – Horace Lamb 422 (via Hub Central) 15:30 – 18:00

� Public Lecture Reception – Ingkarni Wardli Atrium 18:00 – 19:00

� Public Lecture – The Braggs Lecture Theatre 19:00 – 20:00

Etienne Ghys (Ecole normale superieure de Lyon)The shape of our planet Earth: a mathematical challenge!

14

Wed 5 December 2018


2. Algebra


15:30 James East (Western Sydney University)Lattice paths and submonoids of Z2 (p. 56)

16:00 Yeeka Yaus (The University of Sydney)Coxeter Systems for which the Brink-Howlett automaton is minimal (p. 59)

16:30 Alex Bishops (University of Technology, Sydney)Formal languages in group co-word problems (p. 56)

17:00 Ambily Ambattu Asokan (Cochin University of Science and Technology)On von Neumann regularity of simple flat Leavitt path algebras (p. 56)

17:30 Faezeh Alizadehs (Shahid Rajaee Teacher Training University)Linear codes from matrices: answering a question of Glasby and Praeger (p. 56)


Ligertwood 316

15:30 Zlatko Jovanoski (University of New South Wales Canberra)Population dynamics in a variable environment (p. 60)

16:30 Mark Nelson (University of Wollongong)No Jab, no pay (p. 61)

17:00 Kieran Clancy (Flinders University)Choosing investment frequency to minimise brokerage costs (p. 60)

17:30 William Erik Pettersson (University of Glasgow)Large Scale Kidney Exchange Programme Models: Saving Lives with IntegerProgramming (p. 62)

4. Category Theory


15:30 Marcy Robertson (The University of Melbourne)A new class of coloured modular operads (p. 64)

16:00 David Gepner (The University of Melbourne)Analytic monads and infinity operads (p. 64)



15:30 Jerome Droniou (Monash University)What the second Strang lemma and the Aubin-Nitsche trick should be (p. 66)

16:30 Markus Hegland (Australian National University)Numerical linear algebra and the solution of systems of polynomial equations (p. 67)

17:00 Hanz Martin Chengs (Monash University)A combined GDM-ELLAM-MMOC (GEM) scheme for advection dominated PDEs (p.66)

17:30 Alex Newcombes (Flinders University)QuickCross - a crossing minimisation heuristic based on vertex insertion (p. 67)



15:30 Kumbu Dorjis (University of New England)Three-dimensional Sasakian structures and point-extension of monopoles (p. 69)

16:00 Michael Eastwood (The University of Adelaide)The exceptional aerobatics of flying saucers (p. 69)

16:30 Krzysztof Krakowski (Cardinal Stefan Wyszynski University in Warsaw)Properties of some quasi-geodesics on Stiefel manifolds (p. 70)

15

Wed 5 December 2018

17:00 David Baraglia (The University of Adelaide)A gluing formula for families Seiberg-Witten invariants (p. 69)

17:30 Gerd Schmalz (University of New England)A criterion for local embeddability of 3-dimensional CR-structures (p. 71)

7. Dynamical Systems and Ergodic Theory

Ligertwood 214 Piper Alderman Room

15:30 Michael Small (The University of Western Australia)Characterising Chimeras by Constructing Networks (p. 73)

16:00 Renaud Leplaideur (Universite de la Nouvelle Caledonie)Recent results in Thermodynamic Formalism (p. 72)

16:30 Robert Marangell (The University of Sydney)Travelling waves in a model for tumor invasion with the acid-mediation hypothesis (p.72)

17:00 Timothy Robertss (The University of Sydney)Stable nonphysical waves in a model of tumour invasion (p. 72)

17:30 Fawwaz Bataynehs (University of Queensland)Quasi-compactness and invariant measures for random dynamical systems of Jablonskimaps (p. 72)



15:30 Shaymaa Shawkat Kadhim Al-shakarchis (University of New South Wales)Isomorphisms of AC(σ) spaces for linear graphs (p. 74)

16:00 David Leonard Brooks (The University of Adelaide)Computations in Higher Twisted K-theory (p. 75)

16:30 Johnny Lims (The University of Adelaide)Pontryagin duality in higher Aharonov-Bohm effect (p. 76)

17:00 Nathan Brownlowe (The University of Sydney)Can we reconstruct a directed graph from its Toeplitz algebra? (p. 75)

17:30 Elizabeth Bradfords (University of South Australia)An application of recursive algorithm for inversion of linear operator pencils (p. 74)



15:30 Kwok-Kun Kwong (The University of Sydney)Some sharp Levy-Gromov type isoperimetric inequalities (p. 78)

16:00 Pedram Hekmati (The University of Auckland)Higgs bundles and foliations (p. 78)

16:30 Romina Melisa Arroyo (University of Queensland)The long-time behaviour of the pluriclosed flow on Lie groups (p. 78)

17:00 Yuhan Wus (University of Wollongong)Length-constrained curve diffusion (p. 79)



15:30 Dominic Tates (The University of Sydney)Compactification of the Space of Convex Projective Structures on Surfaces (p. 82)

16:00 Adam Woods (The University of Melbourne)Oriented geodesics in the three-sphere (p. 82)

16:30 Sophie Hams (Monash University)Triangulations of Solid Tori and Dehn Fillings (p. 80)

17:00 Vanessa Robins (Australian National University)Tiling the Euclidean and Hyperbolic planes with ribbons (p. 81)

16

Wed 5 December 2018

17:30 Chi-Kwong Fok (The University of Adelaide)Twisted K-theory of compact Lie groups and extended Verlinde algebras (p. 80)


Ligertwood 111

15:30 Tran Vu Khanh (University of Wollongong)Bergman and Bergman-Toeplitz operators on pseudoconvex domains (p. 84)

16:00 Anh Bui (Macquarie University)Sharp weighted estimates for square functions associated to operators on homogeneousspaces (p. 83)

16:30 Geetika Verma (University of South Australia)An inversion technique for linear operator pencils in Hilbert space (p. 84)


Ligertwood 112

15:30 Yang Shi (Flinders University)Certain subgroups of the Coxeter groups and symmetry of discrete integrable equations(p. 85)

16:00 Paul Zinn-Justin (The University of Melbourne)Schubert calculus and quantum integrable systems (p. 86)

16:30 Peter Forrester (The University of Melbourne)Some exact Lyapunov exponents for random matrix products (p. 85)


Engineering North N132

16:00 Nicholas Beaton (The University of Melbourne)Knotting probabilities for polygons in lattice tubes (p. 93)

16:30 Jeongwhan Choi (Korea University)Capillary-Gravity Surface over a Bump: Critical Surface Tension (p. 93)

17:00 Zongzheng Zhou (Monash University)Two-point functions of random walk models on high-dimensional boxes (p. 94)

17:30 Timothy Garoni (Monash University)A limit theorem for the coupling time of the stochastic Ising model (p. 94)

16. Number Theory

Ingkarni Wardli B17

15:30 Ayreena Bakhtawars (La Trobe University)On the growth of product of partial quotients (p. 95)

16:00 Philip Boss (La Trobe University)Hausdorff Measure and Dirichlet Non-Improvable Numbers (p. 95)

16:30 Thomas Morrill (UNSW Canberra)Overpartitions (p. 96)

17:00 Timothy Trudgian (UNSW Canberra)Zeroes of the zeta-function: mind the gap! (p. 96)

17:30 Marley Youngs (University of New South Wales)On multiplicative independence of rational function iterates (p. 96)

17. Optimisation


15:30 Alexander Kruger (Federation University Australia)Characterizations of Holder Error Bounds (p. 99)

16:00 Thi Hoa Buis (Federation University Australia)Generalized convexity (p. 97)

17

Wed 5 December 2018

16:30 Cuong Nguyen Duys (Federation University Australia)Nonlinear parametric error bounds (p. 100)

17:00 Theo Bendits (The University of Newcastle)Doubleton Projections in Hilbert Spaces (p. 97)

17:30 David Kirszenblats (The University of Melbourne)A variational approach to the Dubins traveling salesman problem (p. 98)


Ingkarni Wardli B18

15:30 Ilze Ziedins (The University of Auckland)Stochastic networks with selfish routing and information feedback (p. 105)

16:30 Oscar Peraltas (Technical University of Denmark)A fluid flow model with RAP components (p. 104)

17:00 Liam Hodgkinsons (University of Queensland)Central limit theorems for dynamic random graph models (p. 103)

17:30 Graham Brightwell (London School of Economics)Long-term concentration of measure and the cut-off phenomenon (p. 102)



15:30 Edmund Xian Chen Hengs (Australian National University)Braid group action on triangulated categories (p. 107)

16:00 Matthew James Spongs (The University of Melbourne)Two models of equivariant elliptic cohomology (p. 108)

16:30 Saul Freedmans (The University of Western Australia)p-groups related to exceptional Chevalley groups (p. 106)

17:00 Joel Gibsons (The University of Sydney)The Product Monomial Crystal (p. 106)

17:30 Anthony Henderson (The University of Sydney)Complementary symmetry for Slodowy varieties (p. 107)

18

Thu 6 December 2018

� Morning Special Sessions

2. Algebra


09:00 Robert McDougall (University of the Sunshine Coast)On Kurosh-Amitsur and base radical classes for a non-associative setting (p. 58)

09:30 Lauren Thorntons (University of the Sunshine Coast)Some results differentiating Kurosh-Amitsur and base radical classes (p. 59)

10:00 Neeraj Kumars (IIT Bombay)Koszul and Cohen-Macaulay properties of residual intersections (p. 58)


Ligertwood 316

09:00 Benjamin Maldons (The University of Newcastle)Modelling Dye-Sensitized Solar Cells by Nonlinear Diffusion (p. 61)

09:30 Vanessa Robins (Australian National University)Insights from the persistent homology analysis of porous and granular materials (p. 62)

10:00 Ilknur Tulunay (University of Technology, Sydney)ST-metric estimation of factor weights (p. 63)

4. Category Theory


09:00 Alexander Campbell (Macquarie University)Bicategories vs Rezk’s weak 2-categories (p. 64)

09:30 Dominic Weillers (Australian National University)Algebras in Braided Tensor categories and Embedded surfaces (p. 65)

10:00 Ivo De Los Santos Vekemanss (Australian National University)The slice filtration and spectral sequence (p. 64)



09:00 William McLean (University of New South Wales)A second-order time stepping scheme for fractional diffusion problems (p. 67)

09:30 Hailong Guo (The University of Melbourne)Recovery based finite element method for fourth-order PDEs (p. 66)

10:00 Quoc Thong Le Gia (University of New South Wales)Stochastic Navier-Stokes equations on a thin spherical domain (p. 67)

19

Thu 6 December 2018



09:00 Keegan Floods (The University of Auckland)Scalar curvature and projective compactification (p. 69)

09:30 Daniel Snells (The University of Auckland)Distinguished curves in projective and conformal geometry (p. 71)

10:00 Anthony Shane Marshalls (Flinders University)An Information Geometric Approach To Pulse-Doppler Sensor Optimisation (p. 70)


Ligertwood 214 Piper Alderman Room

09:00 Dave Smith (Yale-NUS College)Dispersive quantisation (p. 73)

09:30 Peter Cudmore (The University of Melbourne)‘Systems all the way down’: Managing Complexity with BondGraphTools (p. 72)

10:00 Cecilia Gonzalez-Tokman (The University of Queensland)Lyapunov spectrum of Perron-Frobenius operator cocycles (p. 72)



09:00 Michael Arthur Mampustis (University of Wollongong)Equilibrium in operator algebraic dynamical systems (p. 76)

09:30 Nicholas Seatons (University of Wollongong)A Dixmier-Douady Theory for Fell Algebras and their associated Brauer Group (p. 77)

10:00 Thomas Scheckters (University of New South Wales)A Noncommutative Generalisation of a Problem of Steinhaus (p. 77)



09:00 James McCoy (The University of Newcastle)Closed ideal planar curves (p. 79)

09:30 Ramiro Augusto Lafuente (The University of Queensland)Hermitian curvature flow on complex Lie groups (p. 78)

10:00 Yong Wei (Australian National University)Volume preserving flow and geometric inequalities in hyperbolic space (p. 79)



09:00 Iva Halacheva (The University of Melbourne)Virtual and welded tangles via operads (p. 80)

09:30 Boris Lishak (The University of Sydney)Trisections and their complexity (p. 81)

10:00 David G Glynn (Flinders University)Particles of the first generation (p. 80)


Ligertwood 112

10:00 Yury Stepanyants (University of Southern Queensland)Helical solitons in vector modified Kortewegde Vries equations (p. 86)

20

Thu 6 December 2018


Ligertwood 216 Sarawak Room

09:00 Danya Rose (The University of Sydney)Who cares? Or, when does paternal care arise in primates? (p. 87)

09:30 Anthony John Gallos (The University of Adelaide)Modelling Non-Uniform Growth in Cylindrical Yeast Colonies (p. 87)

10:00 Mike Chen (The University of Adelaide)Multiscale modelling of fibre-reinforced hydrogels for tissue engineering (p. 87)



09:00 Heather Lonsdale (Curtin University)Choose-your-own assessment (p. 90)

09:30 Amie Albrecht (University of South Australia)Learning to Communicate and Communicating to Learn (p. 89)

10:00 Simon James (Deakin University)Benefits and challenges of peer-assessment for online subjects (p. 90)

16. Number Theory

Ingkarni Wardli B17

09:00 Nicole Sutherland (The University of Sydney)The efficient computation of Splitting Fields using Galois groups (p. 96)

09:30 Mumtaz Hussain (La Trobe University)Measure theoretic laws in Diophantine approximation (p. 96)

17. Optimisation


08:30 Ryan Loxton (Curtin University)Minimizing Equipment Shutdowns in Oil and Gas Campaign Maintenance (p. 99)

09:00 Belinda Spratt (Queensland University of Technology)Reducing post-surgery recovery bed occupancy through an analytical prediction model(p. 101)

09:30 William Erik Pettersson (University of Glasgow)Multi-objective mixed integer programming: An exact algorithm (p. 100)

10:00 Guoyin Li (University of New South Wales)Calculus of Kurdyka-Lojasiewicz exponent and its applications to sparse optimisation(p. 99)


Ingkarni Wardli B18

09:00 Volodymyr Vaskovychs (La Trobe University)On asymptotic behavior of weighted functionals of long-range dependent random fieldson spheres (p. 105)

09:30 Yi-Lung Chens (University of New South Wales)Sampling via Regenerative Chain Monte Carlo (p. 102)

10:00 Peter Taylor (The University of Melbourne)Why is Kemeny’s constant a constant? (p. 104)

21

Thu 6 December 2018



08:30 Yusra Naqvi (The University of Sydney)A product formula for certain coefficients of Macdonald polynomials (p. 108)

09:00 Michael Ehrig (The University of Sydney)Finite dimensional representations of orthosymplectic supergroups (p. 106)

09:30 Travis Scrimshaw (The University of Queensland)Crystal structures for symmetric Grothendieck polynomials (p. 108)

10:00 Anna Romanov (The University of Sydney)An orbit model for the spectra of nilpotent Gelfand pairs (p. 108)



11:00 I Hinke Osinga (The University of Auckland)

Robust chaos: a tale of blenders, their computation, and their destruction


12:00 I Renato Ghini Bettiol (City University of New York)

How to find non-trivial solutions out of trivial ones


� AGM – Horace Lamb Lecture Theatre 14:00 – 15:30



16:00 I Regina Burachik (University of South Australia)

Maximal Monotonicity versus Convexity: A fruitful interplay


17:00 I Etienne Ghys (Ecole normale superieure de Lyon)

The topology of real analytic curves in the plane

� Conference Dinner – National Wine Centre of Australia 19:00 – 23:00

22

Fri 7 December 2018

� Morning Special Sessions



09:00 Zahra Afsar (The University of Sydney)Equilibrium states on Higher-rank Toeplitz noncommutative solenoids (p. 74)

09:30 Fei Han (National University of Singapore)Modular invariants for proper actions (p. 76)

16. Number Theory

Ingkarni Wardli B17

09:00 Min Sha (Macquarie University)Carmichael polynomials over finite fields (p. 96)

09:30 Anand Rajendra Deopurkar (Australian National University)On the geometric Steinitz problem (p. 95)


Ingkarni Wardli B18

09:00 Angus Hamilton Lewiss (The University of Adelaide)Algorithms for Markovian Regime Switching models for electricity prices (p. 103)

09:30 Andriy Olenko (La Trobe University)Statistics and filter transforms of Gegenbauer-type processes (p. 104)



10:30 I Josef Dick (University of New South Wales)

Numerical methods for partial differential equations with random coefficients


11:30 I Nageswari Shanmugalingam (University of Cincinnati)

Analysis in non-smooth spaces using paths



23

Fri 7 December 2018


2. Algebra


13:30 David Gepner (The University of Melbourne)Algebraic K-theory, endomorphisms, and Witt vectors (p. 57)

14:30 George Willis (The University of Newcastle)Solvable locally compact contraction groups are nilpotent (p. 59)

15:00 Stephen Glasby (The University of Western Australia)Permutations with orders coprime to a given integer (p. 57)

16:00 Michael Giudici (The University of Western Australia)Subgroups of classical groups that are transitive on subspaces (p. 57)

16:30 David Robertson (The University of Newcastle)Locally compact piecewise full groups (p. 58)

17:00 Tim Stokes (University of Waikato)What is a partial semigroup? (p. 58)



13:30 Michael Haythorpe (Flinders University)Using a crossing minimisation heuristic to solve some open problems (p. 66)



13:30 Peter Vassiliou (Australian National University)Symmetry and Geometric Control Theory (p. 71)

14:00 Michael Murray (The University of Adelaide)Signs for Real and equivariant gerbes (p. 71)

14:30 Alessandro Ottazzi (University of New South Wales)Nilpotent Lie groups and metric geometry (p. 71)



13:30 Silvestru Sever Dragomir (Victoria University)Inequalities in Hermitian unital Banach ∗-algebras (p. 76)

14:00 Ian Doust (University of New South Wales)Asymptotic negative type properties of finite ultrametric spaces (p. 75)

14:30 Guo Chuan Thiang (The University of Adelaide)Crystallographic T-duality and super Baum-Connes conjecture (p. 77)

15:00 Matthias Ludewig (The University of Adelaide)The Chern character of differential graded algebras and an Index Theorem (p. 76)

16:00 Arnaud Brothier (UNSW Sydney)Unitary representations of the Thompson group constructed with a category/functormethod due to Jones (p. 75)

16:30 Faezeh Alizadehs (Shahid Rajaee Teacher Training University)Some results on Roman 2-domination in graphs (p. 74)



13:30 Matthias Ludewig (The University of Adelaide)Supersymmetric path integrals: Integrating differential forms on the loop space (p. 81)

14:00 Chen Guanheng (The University of Adelaide)Cobordism map on PFH induced by elementary Lefschetz fibration (p. 80)

24

Fri 7 December 2018

14:30 Jian He (Monash University)Counting Non-Crossing Partitions on Surfaces (p. 81)



13:30 Greg Oates (University of Tasmania)Conceptual Considerations in the Transition to University Mathematics: The Case forLimits as a Threshold Concept (p. 92)

14:00 Jelena Schmalz (University of New England)Transition between school and university placement test and bridging course (p. 92)

14:30 Ross Moore (Macquarie University)Authoring accessible ‘Tagged PDF documents using LATEX (p. 91)

15:00 Chi Mak (University of New South Wales)Comparing the Quality of Learning Outcomes (p. 91)

16:00 Diane Donovan (The University of Queensland)Educating On-line Software (p. 89)

16:30 Deborah Jackson (La Trobe University)Reflections on a kaleidoscope of multi-faceted, cross-disciplinary mathematics support.Feeding the growing appetite (p. 90)

17. Optimisation


13:30 Phil Howlett (University of South Australia)The two-train separation problem (p. 98)

14:00 Tansu Alpcan (The University of Melbourne)Game Theory and Machine Learning for Complex Networked Systems (p. 97)

14:30 Andrew Craig Eberhard (Royal Melbourne Institute of Technology)A fixed point operator in discrete optimisation (p. 97)

15:00 Janosch Rieger (Monash University)Electrical impedance tomography for unknown domains (p. 100)

16:00 Minh N. Dao (The University of Newcastle)Adaptive Douglas-Rachford splitting algorithm for the sum of two operators (p. 97)

16:30 Chayne Planiden (University of Wollongong)A Derivative-free VU-algorithm for Convex Functions (p. 100)

17:00 Wilhelm Freire (Universidade Federal de Juiz de Fora)The Interior Epigraph Directions Algorithm for Nonsmooth and NonconvexConstrained Optimization and applications (p. 98)

17:30 Yalcin Kaya (University of South Australia)Constraint Splitting and Projection Methods for Optimal Control (p. 98)


Ingkarni Wardli B18

13:30 Sarat Babu Moka (The University of Queensland)Perfect Sampling for Gibbs Point Processes using Partial Rejection Sampling (p. 104)

14:00 Samuel Cohen (The University of Oxford)Statistical Uncertainty in Decision Making (p. 102)

14:30 Hermanus Marinus Jansen (The University of Queensland)The power of QED-like scaling for many-server queues in a random environment (p.103)

25

Fri 7 December 2018



13:30 Asilata Bapat (Australian National University)Recollement of perverse sheaves on real hyperplane arrangements (p. 106)

14:00 Thomas Gobet (The University of Sydney)A Soergel-like category for complex reflection groups of rank one (p. 107)

14:30 Valentin Buciumas (The University of Queensland)Quantum polynomial functors (p. 106)

26

Plenary Lectures in The Braggs Lecture Theatre

B Tue 4 December 2018

11:00 I Geordie Williamson (The University of Sydney)

Semi-simplicity in representation theory

12:00 I Malwina Luczak (The University of Melbourne)

Near-criticality in mathematical models of epidemics

17:00 I Steven Sherwood (University of New South Wales)

Recent Advances in Climate Sensitivity

B Wed 5 December 2018

09:30 I Natalie Thamwattana (The University of Newcastle)

A mathematical journey into nanoscience and nanotechnology

11:00 I Manjunath Krishnapur (Indian Institute of Science Bangalore)

Nodal sets of eigenfunctions of the Laplacian, with randomness

12:00 I Joan Licata (Australian National University)

Just Enough Twisting

B Thu 6 December 2018

11:00 I Hinke Osinga (The University of Auckland)

Robust chaos: a tale of blenders, their computation, and their destruction

12:00 I Renato Ghini Bettiol (City University of New York)

How to find non-trivial solutions out of trivial ones

16:00 I Regina Burachik (University of South Australia)

Maximal Monotonicity versus Convexity: A fruitful interplay

17:00 I Etienne Ghys (Ecole normale superieure de Lyon)

The topology of real analytic curves in the plane

B Fri 7 December 2018

10:30 I Josef Dick (University of New South Wales)

Numerical methods for partial differential equations with random coefficients

11:30 I Nageswari Shanmugalingam (University of Cincinnati)

Analysis in non-smooth spaces using paths

27

Special Session 1: Algebra

Organisers Daniel Chan, Roozbeh Hazrat, Mircea Voineagu

Keynote Talks


13:30 David Gepner (The University of Melbourne)Algebraic K-theory, endomorphisms, and Witt vectors (p. 57)

Contributed Talks


14:00 Jeremy Sumner (University of Tasmania)Markov association schemes (p. 58)

14:30 Alejandra Garrido (The University of Newcastle)Hausdorff dimension and normal subgroups of free-like pro-p groups (p. 57)

15:30 Timothy Peter Bywaterss (The University of Sydney)Spaces at infinity for hyperbolic totally disconnected locally compact groups (p. 56)

16:00 Carlisle King (The University of Western Australia)Finite simple images of finitely presented groups (p. 58)

16:30 Stephan Tornier (The University of Newcastle)Totally disconnected, locally compact groups from transcendental field extensions (p.59)


15:30 James East (Western Sydney University)Lattice paths and submonoids of Z2 (p. 56)

16:00 Yeeka Yaus (The University of Sydney)Coxeter Systems for which the Brink-Howlett automaton is minimal (p. 59)

16:30 Alex Bishops (University of Technology, Sydney)Formal languages in group co-word problems (p. 56)

17:00 Ambily Ambattu Asokan (Cochin University of Science and Technology)On von Neumann regularity of simple flat Leavitt path algebras (p. 56)

17:30 Faezeh Alizadehs (Shahid Rajaee Teacher Training University)Linear codes from matrices: answering a question of Glasby and Praeger (p. 56)


09:00 Robert McDougall (University of the Sunshine Coast)On Kurosh-Amitsur and base radical classes for a non-associative setting (p. 58)

09:30 Lauren Thorntons (University of the Sunshine Coast)Some results differentiating Kurosh-Amitsur and base radical classes (p. 59)

10:00 Neeraj Kumars (IIT Bombay)Koszul and Cohen-Macaulay properties of residual intersections (p. 58)


14:30 George Willis (The University of Newcastle)Solvable locally compact contraction groups are nilpotent (p. 59)

28

1. Algebra

15:00 Stephen Glasby (The University of Western Australia)Permutations with orders coprime to a given integer (p. 57)

16:00 Michael Giudici (The University of Western Australia)Subgroups of classical groups that are transitive on subspaces (p. 57)

16:30 David Robertson (The University of Newcastle)Locally compact piecewise full groups (p. 58)

17:00 Tim Stokes (University of Waikato)What is a partial semigroup? (p. 58)

29

Special Session 2: Applied and Industrial Mathematics

Organisers Mark Nelson, Harvinder Sidhu

Keynote Talks


15:30 Zlatko Jovanoski (University of New South Wales Canberra)Population dynamics in a variable environment (p. 60)

Contributed Talks


14:00 Andrei Ermakovs (University of Southern Queensland)Mathematical problems of long wave transformation in a coastal zone with a variablebathymetry (p. 60)

14:30 Ajini Galapitages (University of South Australia)Optimal scheduling of trains using connected driver advice system (p. 60)

15:30 Mark Joseph McGuinness (Victoria University of Wellington)MMM, microwaves measure moisture (p. 61)

16:00 Yvonne Stokes (The University of Adelaide)A coupled flow and temperature model for fibre drawing (p. 62)

16:30 Sevvandi Priyanvada Kandanaarachchi (Monash University)About outlier detection (p. 61)


16:30 Mark Nelson (University of Wollongong)No Jab, no pay (p. 61)

17:00 Kieran Clancy (Flinders University)Choosing investment frequency to minimise brokerage costs (p. 60)

17:30 William Erik Pettersson (University of Glasgow)Large Scale Kidney Exchange Programme Models: Saving Lives with IntegerProgramming (p. 62)


09:00 Benjamin Maldons (The University of Newcastle)Modelling Dye-Sensitized Solar Cells by Nonlinear Diffusion (p. 61)

09:30 Vanessa Robins (Australian National University)Insights from the persistent homology analysis of porous and granular materials (p. 62)

10:00 Ilknur Tulunay (University of Technology, Sydney)ST-metric estimation of factor weights (p. 63)

30

Special Session 3: Category Theory

Organisers Alexander Campbell, David Roberts

Contributed Talks


14:00 Yuki Maeharas (Macquarie University)Inner horns for 2-quasi-categories (p. 64)

14:30 Michelle Strumilas (The University of Melbourne)Infinity Cyclic Operads (p. 64)

15:30 Danny Stevenson (The University of Adelaide)The right cancellation property of the class of inner anodyne maps (p. 64)


15:30 Marcy Robertson (The University of Melbourne)A new class of coloured modular operads (p. 64)

16:00 David Gepner (The University of Melbourne)Analytic monads and infinity operads (p. 64)


09:00 Alexander Campbell (Macquarie University)Bicategories vs Rezk’s weak 2-categories (p. 64)

09:30 Dominic Weillers (Australian National University)Algebras in Braided Tensor categories and Embedded surfaces (p. 65)

10:00 Ivo De Los Santos Vekemanss (Australian National University)The slice filtration and spectral sequence (p. 64)

31

Special Session 4: Computational Mathematics

Organisers Bishnu Lamichhane, Quoc Thong Le Gia

Keynote Talks


15:30 Jerome Droniou (Monash University)What the second Strang lemma and the Aubin-Nitsche trick should be (p. 66)

Contributed Talks


14:30 Garry Newsam (The University of Adelaide)A review of some approximation schemes used in FFTs on non-uniform grids (p. 67)

15:30 Robert Womersley (University of New South Wales)Using spherical t-designs and `q minimization for recovery of sparse signals on thesphere (p. 68)

16:00 Yuguang Wang (University of New South Wales)Sparse Isotropic Regularization for Spherical Harmonic Representations of RandomFields on the Sphere (p. 68)

16:30 Janosch Rieger (Monash University)Integrating semilinear parabolic differential inclusions with one-sided Lipschitznonlinearities (p. 67)


16:30 Markus Hegland (Australian National University)Numerical linear algebra and the solution of systems of polynomial equations (p. 67)

17:00 Hanz Martin Chengs (Monash University)A combined GDM-ELLAM-MMOC (GEM) scheme for advection dominated PDEs (p.66)

17:30 Alex Newcombes (Flinders University)QuickCross - a crossing minimisation heuristic based on vertex insertion (p. 67)


09:00 William McLean (University of New South Wales)A second-order time stepping scheme for fractional diffusion problems (p. 67)

09:30 Hailong Guo (The University of Melbourne)Recovery based finite element method for fourth-order PDEs (p. 66)

10:00 Quoc Thong Le Gia (University of New South Wales)Stochastic Navier-Stokes equations on a thin spherical domain (p. 67)


13:30 Michael Haythorpe (Flinders University)Using a crossing minimisation heuristic to solve some open problems (p. 66)

32

Special Session 5: Differential Geometry

Organisers Wolfgang Globke, Yuri Nikolayevsky

Contributed Talks


14:00 Renato Ghini Bettiol (City University of New York)Convex Algebraic Geometry of Curvature Operators (p. 69)

14:30 Romina Melisa Arroyo (University of Queensland)The Alekseevskii conjecture: Overview and open questions (p. 69)

15:30 Ramiro Augusto Lafuente (The University of Queensland)Homogeneous Einstein manifolds via a cohomogeneity-one approach (p. 70)

16:00 Owen Dearricott (The University of Melbourne)Positive curvature in dimension 7 (p. 69)

16:30 Kelli Francis-Staites (The University of Oxford)Corners in C∞-Algebraic Geometry (p. 70)


15:30 Kumbu Dorjis (University of New England)Three-dimensional Sasakian structures and point-extension of monopoles (p. 69)

16:00 Michael Eastwood (The University of Adelaide)The exceptional aerobatics of flying saucers (p. 69)

16:30 Krzysztof Krakowski (Cardinal Stefan Wyszynski University in Warsaw)Properties of some quasi-geodesics on Stiefel manifolds (p. 70)

17:00 David Baraglia (The University of Adelaide)A gluing formula for families Seiberg-Witten invariants (p. 69)

17:30 Gerd Schmalz (University of New England)A criterion for local embeddability of 3-dimensional CR-structures (p. 71)


09:00 Keegan Floods (The University of Auckland)Scalar curvature and projective compactification (p. 69)

09:30 Daniel Snells (The University of Auckland)Distinguished curves in projective and conformal geometry (p. 71)

10:00 Anthony Shane Marshalls (Flinders University)An Information Geometric Approach To Pulse-Doppler Sensor Optimisation (p. 70)


13:30 Peter Vassiliou (Australian National University)Symmetry and Geometric Control Theory (p. 71)

14:00 Michael Murray (The University of Adelaide)Signs for Real and equivariant gerbes (p. 71)

14:30 Alessandro Ottazzi (University of New South Wales)Nilpotent Lie groups and metric geometry (p. 71)

33

Special Session 6: Dynamical Systems and ErgodicTheory

Organisers Cecilia Gonzalez-Tokman, Robert Marangell

Contributed Talks


15:30 Michael Small (The University of Western Australia)Characterising Chimeras by Constructing Networks (p. 73)

16:00 Renaud Leplaideur (Universite de la Nouvelle Caledonie)Recent results in Thermodynamic Formalism (p. 72)

16:30 Robert Marangell (The University of Sydney)Travelling waves in a model for tumor invasion with the acid-mediation hypothesis (p.72)

17:00 Timothy Robertss (The University of Sydney)Stable nonphysical waves in a model of tumour invasion (p. 72)

17:30 Fawwaz Bataynehs (University of Queensland)Quasi-compactness and invariant measures for random dynamical systems of Jablonskimaps (p. 72)


09:00 Dave Smith (Yale-NUS College)Dispersive quantisation (p. 73)

09:30 Peter Cudmore (The University of Melbourne)‘Systems all the way down’: Managing Complexity with BondGraphTools (p. 72)

10:00 Cecilia Gonzalez-Tokman (The University of Queensland)Lyapunov spectrum of Perron-Frobenius operator cocycles (p. 72)

34

Special Session 7: Functional Analysis, OperatorAlgebra, Non-commutative Geometry

Organisers Zahra Afsar, Peter Hochs

Keynote Talks


14:00 Mathai Varghese (The University of Adelaide)The magnetic spectral gap-labelling conjecture and some recent progess (p. 77)

Contributed Talks


15:30 Jessica Murphys (The University of Sydney)C*-algebras associated to graphs of groups (p. 77)

16:00 Becky Armstrongs (The University of Sydney)A twisted tale of topological k-graph C*-algebras (p. 74)

16:30 Raveen Daminda de Silvas (University of New South Wales)Maximum Generalised Roundness of Random Graphs (p. 75)


15:30 Shaymaa Shawkat Kadhim Al-shakarchis (University of New South Wales)Isomorphisms of AC(σ) spaces for linear graphs (p. 74)

16:00 David Leonard Brooks (The University of Adelaide)Computations in Higher Twisted K-theory (p. 75)

16:30 Johnny Lims (The University of Adelaide)Pontryagin duality in higher Aharonov-Bohm effect (p. 76)

17:00 Nathan Brownlowe (The University of Sydney)Can we reconstruct a directed graph from its Toeplitz algebra? (p. 75)

17:30 Elizabeth Bradfords (University of South Australia)An application of recursive algorithm for inversion of linear operator pencils (p. 74)


09:00 Michael Arthur Mampustis (University of Wollongong)Equilibrium in operator algebraic dynamical systems (p. 76)

09:30 Nicholas Seatons (University of Wollongong)A Dixmier-Douady Theory for Fell Algebras and their associated Brauer Group (p. 77)

10:00 Thomas Scheckters (University of New South Wales)A Noncommutative Generalisation of a Problem of Steinhaus (p. 77)


09:00 Zahra Afsar (The University of Sydney)Equilibrium states on Higher-rank Toeplitz noncommutative solenoids (p. 74)

09:30 Fei Han (National University of Singapore)Modular invariants for proper actions (p. 76)

13:30 Silvestru Sever Dragomir (Victoria University)Inequalities in Hermitian unital Banach ∗-algebras (p. 76)

14:00 Ian Doust (University of New South Wales)Asymptotic negative type properties of finite ultrametric spaces (p. 75)

35


14:30 Guo Chuan Thiang (The University of Adelaide)Crystallographic T-duality and super Baum-Connes conjecture (p. 77)

15:00 Matthias Ludewig (The University of Adelaide)The Chern character of differential graded algebras and an Index Theorem (p. 76)

16:00 Arnaud Brothier (UNSW Sydney)Unitary representations of the Thompson group constructed with a category/functormethod due to Jones (p. 75)

16:30 Faezeh Alizadehs (Shahid Rajaee Teacher Training University)Some results on Roman 2-domination in graphs (p. 74)

36

Special Session 8: Geometric Analysis

Organisers Guanheng Chen, Chi-Kwong Fok

Contributed Talks


14:00 Miles Simon (Magdeburg University)Some integral estimates for Ricci flow in four dimensions (p. 79)

14:30 Ahnaf Tajwar Tahabubs (The University of Adelaide)Reduced SU(2) Seiberg-Witten Equations compared to SU(2) Ginzburg-Landauequations (p. 79)

15:30 Brett Parker (Monash University)Regularity of the dbar equation in degenerating families (p. 79)

16:00 David Hartley (University of Wollongong)On the Existence of Stable Unduloids of Dimension Eight (p. 78)


15:30 Kwok-Kun Kwong (The University of Sydney)Some sharp Levy-Gromov type isoperimetric inequalities (p. 78)

16:00 Pedram Hekmati (The University of Auckland)Higgs bundles and foliations (p. 78)

16:30 Romina Melisa Arroyo (University of Queensland)The long-time behaviour of the pluriclosed flow on Lie groups (p. 78)

17:00 Yuhan Wus (University of Wollongong)Length-constrained curve diffusion (p. 79)


09:00 James McCoy (The University of Newcastle)Closed ideal planar curves (p. 79)

09:30 Ramiro Augusto Lafuente (The University of Queensland)Hermitian curvature flow on complex Lie groups (p. 78)

10:00 Yong Wei (Australian National University)Volume preserving flow and geometric inequalities in hyperbolic space (p. 79)

37

Special Session 9: Geometry and Topology

Organisers Zsuzsanna Dancso, Jessica Purcell

Keynote Talks


14:00 Brett Parker (Monash University)Tropical geometry, the topological vertex, and Gromov-Witten invariants of Calabi-Yau3-folds, (p. 81)

Contributed Talks


15:30 Benjamin Burton (University of Queensland)Knot tabulation: a software odyssey (p. 80)

16:00 Anne Thomas (The University of Sydney)Commensurability classification of certain right-angled Coxeter groups (p. 82)

16:30 Daniel Francis Mansfield (University of New South Wales)Perpendicularity in Ancient Babylon (p. 81)


15:30 Dominic Tates (The University of Sydney)Compactification of the Space of Convex Projective Structures on Surfaces (p. 82)

16:00 Adam Woods (The University of Melbourne)Oriented geodesics in the three-sphere (p. 82)

16:30 Sophie Hams (Monash University)Triangulations of Solid Tori and Dehn Fillings (p. 80)

17:00 Vanessa Robins (Australian National University)Tiling the Euclidean and Hyperbolic planes with ribbons (p. 81)

17:30 Chi-Kwong Fok (The University of Adelaide)Twisted K-theory of compact Lie groups and extended Verlinde algebras (p. 80)


09:00 Iva Halacheva (The University of Melbourne)Virtual and welded tangles via operads (p. 80)

09:30 Boris Lishak (The University of Sydney)Trisections and their complexity (p. 81)

10:00 David G Glynn (Flinders University)Particles of the first generation (p. 80)


13:30 Matthias Ludewig (The University of Adelaide)Supersymmetric path integrals: Integrating differential forms on the loop space (p. 81)

14:00 Chen Guanheng (The University of Adelaide)Cobordism map on PFH induced by elementary Lefschetz fibration (p. 80)

14:30 Jian He (Monash University)Counting Non-Crossing Partitions on Surfaces (p. 81)

38

Special Session 10: Harmonic Analysis

Organisers Anh Bui, Ji Li

Contributed Talks


14:30 Xuan Duong (Macquarie University)BMO spaces associated to operators on non-doubling manifolds with ends (p. 83)

15:30 Neil Kristofer Dizons (The University of Newcastle)Optimisation in the Construction of Symmetric and Cardinal Wavelets on the Line (p.83)

16:00 Hong Chuong Doans (Macquarie University)Maximal operators with generalised Gaussian bounds on non-doubling Riemannianmanifolds with low dimension (p. 83)

16:30 Xing Cheng (Monash University)Scattering of the nonlinear Klein-Gordon equations (p. 83)


15:30 Tran Vu Khanh (University of Wollongong)Bergman and Bergman-Toeplitz operators on pseudoconvex domains (p. 84)

16:00 Anh Bui (Macquarie University)Sharp weighted estimates for square functions associated to operators on homogeneousspaces (p. 83)

16:30 Geetika Verma (University of South Australia)An inversion technique for linear operator pencils in Hilbert space (p. 84)

39

Special Session 11: Integrable Systems

Organisers Nalini Joshi, Milena Radnovic, Yang Shi

Contributed Talks


14:00 Nalini Joshi (The University of Sydney)Hidden solutions of discrete systems (p. 85)

14:30 Remy Alexander Addertons (The Australian National University)A generalized Temperley-Lieb algebra in the chiral Potts model (p. 85)

15:30 Yibing Shens (The University of Queensland)Ground-state energies of the open and closed p+ ip-pairing models from the BetheAnsatz (p. 85)

16:00 Reinout Quispel (La Trobe University)Finding rational integrals of rational discrete maps (p. 85)

16:30 Kenji Kajiwara (Kyushu University)A new framework and extensions of log-aesthetic curves in industrial design byintegrable geometry (p. 85)


15:30 Yang Shi (Flinders University)Certain subgroups of the Coxeter groups and symmetry of discrete integrable equations(p. 85)

16:00 Paul Zinn-Justin (The University of Melbourne)Schubert calculus and quantum integrable systems (p. 86)

16:30 Peter Forrester (The University of Melbourne)Some exact Lyapunov exponents for random matrix products (p. 85)


10:00 Yury Stepanyants (University of Southern Queensland)Helical solitons in vector modified Kortewegde Vries equations (p. 86)

40

Special Session 12: Mathematical Biology

Organisers Mike Chen, Peter Kim

Contributed Talks


15:30 Jeremy Sumner (University of Tasmania)Predicating saturation in models of genome rearrangement in polynomial time (p. 88)

16:00 Yoong Kuan Gohs (University of Technology, Sydney)Pattern Avoidance in Genomics (p. 87)

16:30 Maria Kleshninas (The University of Queensland)Learning advantages in evolutionary games (p. 87)


09:00 Danya Rose (The University of Sydney)Who cares? Or, when does paternal care arise in primates? (p. 87)

09:30 Anthony John Gallos (The University of Adelaide)Modelling Non-Uniform Growth in Cylindrical Yeast Colonies (p. 87)

10:00 Mike Chen (The University of Adelaide)Multiscale modelling of fibre-reinforced hydrogels for tissue engineering (p. 87)

41

Special Session 13: Mathematics Education

Organisers Amie Albrecht, Deborah King, Raymond Vozzo

Contributed Talks


14:00 David Hartley (University of Wollongong)Student learning and feedback in higher education mathematics (p. 90)

14:30 Carolyn Kennett (Macquarie University)Mathematics and Indigenous Culture (p. 90)

15:30 Margaret Marshman (University of the Sunshine Coast)Making mathematics teachers: Beliefs about mathematics and mathematics teachingand learning held by academics who teach future teachers (p. 91)

16:00 Roland Dodd (Central Queensland University)First year engineering mathematics diagnostic testing (p. 89)

16:30 William Guo (Central Queensland University)You can teach old dogs new tricks if you know them well (p. 89)


09:00 Heather Lonsdale (Curtin University)Choose-your-own assessment (p. 90)

09:30 Amie Albrecht (University of South Australia)Learning to Communicate and Communicating to Learn (p. 89)

10:00 Simon James (Deakin University)Benefits and challenges of peer-assessment for online subjects (p. 90)


13:30 Greg Oates (University of Tasmania)Conceptual Considerations in the Transition to University Mathematics: The Case forLimits as a Threshold Concept (p. 92)

14:00 Jelena Schmalz (University of New England)Transition between school and university placement test and bridging course (p. 92)

14:30 Ross Moore (Macquarie University)Authoring accessible ‘Tagged PDF documents using LATEX (p. 91)

15:00 Chi Mak (University of New South Wales)Comparing the Quality of Learning Outcomes (p. 91)

16:00 Diane Donovan (The University of Queensland)Educating On-line Software (p. 89)

16:30 Deborah Jackson (La Trobe University)Reflections on a kaleidoscope of multi-faceted, cross-disciplinary mathematics support.Feeding the growing appetite (p. 90)

42

Special Session 14: Mathematical Physics

Organisers Iwan Jensen, Thomas Quella

Contributed Talks


14:00 Anupam Chaudhuris (Monash University)One-point recursions of Harer-Zagier type (p. 93)

14:30 Arnaud Brothier (UNSW Sydney)Constructions of 1+1-dimensional lattice-gauge theories and the Thompson group (p.93)

15:30 Philip Broadbridge (La Trobe University)The conditionally integrable diffusion equation with nonlinear diffusivity 1/u (p. 93)

16:00 Iwan Jensen (Flinders University)Self-avoiding walks with restricted end-points (p. 94)

16:30 Anthony Mays (The University of Melbourne)Determinantal polynomials, vortices and random matrices: an exercise in experimentalmathematical physics (p. 94)


16:00 Nicholas Beaton (The University of Melbourne)Knotting probabilities for polygons in lattice tubes (p. 93)

16:30 Jeongwhan Choi (Korea University)Capillary-Gravity Surface over a Bump: Critical Surface Tension (p. 93)

17:00 Zongzheng Zhou (Monash University)Two-point functions of random walk models on high-dimensional boxes (p. 94)

17:30 Timothy Garoni (Monash University)A limit theorem for the coupling time of the stochastic Ising model (p. 94)

43

Special Session 15: Number Theory

Organisers Mumtaz Hussain, Min Sha

Keynote Talks


14:00 Ole Warnaar (The University of Queensland)On modular Nekrasov–Okounkov formulas (p. 96)

Contributed Talks


15:30 Florian Breuer (The University of Newcastle)Heights and isogenies of Drinfeld modules (p. 95)

16:00 Matteo Bordignons (University of New South Wales Canberra)Explicit bounds on exceptional zeroes of Dirichlet L-functions (p. 95)

16:30 Michaela Cully-Hugills (University of New South Wales Canberra)Square-free numbers in short intervals (p. 95)


15:30 Ayreena Bakhtawars (La Trobe University)On the growth of product of partial quotients (p. 95)

16:00 Philip Boss (La Trobe University)Hausdorff Measure and Dirichlet Non-Improvable Numbers (p. 95)

16:30 Thomas Morrill (UNSW Canberra)Overpartitions (p. 96)

17:00 Timothy Trudgian (UNSW Canberra)Zeroes of the zeta-function: mind the gap! (p. 96)

17:30 Marley Youngs (University of New South Wales)On multiplicative independence of rational function iterates (p. 96)


09:00 Nicole Sutherland (The University of Sydney)The efficient computation of Splitting Fields using Galois groups (p. 96)

09:30 Mumtaz Hussain (La Trobe University)Measure theoretic laws in Diophantine approximation (p. 96)


09:00 Min Sha (Macquarie University)Carmichael polynomials over finite fields (p. 96)

09:30 Anand Rajendra Deopurkar (Australian National University)On the geometric Steinitz problem (p. 95)

44

Special Session 16: Optimisation

Organisers Yalcin Kaya, Guoyin Li

Keynote Talks


14:00 Marco Antonio Lopez Cerda (Alicante University)A crash course on stability in linear optimization (p. 99)

Contributed Talks


15:30 Helmut Maurer (University of Mnster)Multi-objective Optimal Control Problems in Biomedical Engineering (p. 99)

16:00 Sabine Pickenhain (Brandenburg Technical University Cottbus)Optimal Control on Unbounded Intervals - Fourier-Laguerre Analysis of the Problem(p. 100)

16:30 Vladimir Gaitsgory (Macquarie University)On continuity/discontinuity of the optimal value of a long-run average optimal controlproblem depending on a parameter (p. 98)


15:30 Alexander Kruger (Federation University Australia)Characterizations of Holder Error Bounds (p. 99)

16:00 Thi Hoa Buis (Federation University Australia)Generalized convexity (p. 97)

16:30 Cuong Nguyen Duys (Federation University Australia)Nonlinear parametric error bounds (p. 100)

17:00 Theo Bendits (The University of Newcastle)Doubleton Projections in Hilbert Spaces (p. 97)

17:30 David Kirszenblats (The University of Melbourne)A variational approach to the Dubins traveling salesman problem (p. 98)


08:30 Ryan Loxton (Curtin University)Minimizing Equipment Shutdowns in Oil and Gas Campaign Maintenance (p. 99)

09:00 Belinda Spratt (Queensland University of Technology)Reducing post-surgery recovery bed occupancy through an analytical prediction model(p. 101)

09:30 William Erik Pettersson (University of Glasgow)Multi-objective mixed integer programming: An exact algorithm (p. 100)

10:00 Guoyin Li (University of New South Wales)Calculus of Kurdyka-Lojasiewicz exponent and its applications to sparse optimisation(p. 99)

45

16. Optimisation


13:30 Phil Howlett (University of South Australia)The two-train separation problem (p. 98)

14:00 Tansu Alpcan (The University of Melbourne)Game Theory and Machine Learning for Complex Networked Systems (p. 97)

14:30 Andrew Craig Eberhard (Royal Melbourne Institute of Technology)A fixed point operator in discrete optimisation (p. 97)

15:00 Janosch Rieger (Monash University)Electrical impedance tomography for unknown domains (p. 100)

16:00 Minh N. Dao (The University of Newcastle)Adaptive Douglas-Rachford splitting algorithm for the sum of two operators (p. 97)

16:30 Chayne Planiden (University of Wollongong)A Derivative-free VU-algorithm for Convex Functions (p. 100)

17:00 Wilhelm Freire (Universidade Federal de Juiz de Fora)The Interior Epigraph Directions Algorithm for Nonsmooth and NonconvexConstrained Optimization and applications (p. 98)

17:30 Yalcin Kaya (University of South Australia)Constraint Splitting and Projection Methods for Optimal Control (p. 98)

46

Special Session 17: Probability Theory and StochasticProcesses

Organisers Andrea Collevecchio, Giang Nguyen, Thomas Taimre

Keynote Talks


15:30 Ilze Ziedins (The University of Auckland)Stochastic networks with selfish routing and information feedback (p. 105)

Contributed Talks


14:00 Kais Hamza (Monash University)Directed walk on a randomly oriented lattice (p. 103)

14:30 Kihun Nam (Monash University)Correlated time-changed Levy processes (p. 104)

15:30 Kostya Borovkov (The University of Melbourne)The asymptotics of the large deviation probabilities in the multivariate boundarycrossing problem (p. 102)

16:00 Andrea Collevecchio (Monash University)Branching ruin number (p. 103)

16:30 Lachlan James Bridgess (The University of Adelaide)Markov-modulated random walk search strategies for animal foraging (p. 102)


16:30 Oscar Peraltas (Technical University of Denmark)A fluid flow model with RAP components (p. 104)

17:00 Liam Hodgkinsons (University of Queensland)Central limit theorems for dynamic random graph models (p. 103)

17:30 Graham Brightwell (London School of Economics)Long-term concentration of measure and the cut-off phenomenon (p. 102)


09:00 Volodymyr Vaskovychs (La Trobe University)On asymptotic behavior of weighted functionals of long-range dependent random fieldson spheres (p. 105)

09:30 Yi-Lung Chens (University of New South Wales)Sampling via Regenerative Chain Monte Carlo (p. 102)

10:00 Peter Taylor (The University of Melbourne)Why is Kemeny’s constant a constant? (p. 104)


09:00 Angus Hamilton Lewiss (The University of Adelaide)Algorithms for Markovian Regime Switching (MRS) models for electricity prices (p.103)

09:30 Andriy Olenko (La Trobe University)Statistics and filter transforms of Gegenbauer-type processes (p. 104)

47


13:30 Sarat Babu Moka (The University of Queensland)Perfect Sampling for Gibbs Point Processes using Partial Rejection Sampling (p. 104)

14:00 Samuel Cohen (The University of Oxford)Statistical Uncertainty in Decision Making (p. 102)

14:30 Hermanus Marinus Jansen (The University of Queensland)The power of QED-like scaling for many-server queues in a random environment (p.103)

48

Special Session 18: Representation Theory

Organisers Yaping Yang, Gufang Zhao

Contributed Talks


14:00 Masoud Kamgarpour (University of Queensland)Topology of representation stacks (p. 107)

14:30 Iva Halacheva (The University of Melbourne)Puzzles for restricting Schubert classes to the symplectic Grassmannian (p. 107)

15:30 Alexander Ferdinand Kerschls (The University of Sydney)Inner products on graded Specht modules (p. 107)

16:00 Marvin Kringss (RWTH Aachen University)The p-Part of the Order of an Almost Simple Group of Lie Type (p. 108)

16:30 Seamus Albions (The University of Queensland)The Selberg integral and Macdonald polynomials (p. 106)


15:30 Edmund Xian Chen Hengs (Australian National University)Braid group action on triangulated categories (p. 107)

16:00 Matthew James Spongs (The University of Melbourne)Two models of equivariant elliptic cohomology (p. 108)

16:30 Saul Freedmans (The University of Western Australia)p-groups related to exceptional Chevalley groups (p. 106)

17:00 Joel Gibsons (The University of Sydney)The Product Monomial Crystal (p. 106)

17:30 Anthony Henderson (The University of Sydney)Complementary symmetry for Slodowy varieties (p. 107)


08:30 Yusra Naqvi (The University of Sydney)A product formula for certain coefficients of Macdonald polynomials (p. 108)

09:00 Michael Ehrig (The University of Sydney)Finite dimensional representations of orthosymplectic supergroups (p. 106)

09:30 Travis Scrimshaw (The University of Queensland)Crystal structures for symmetric Grothendieck polynomials (p. 108)

10:00 Anna Romanov (The University of Sydney)An orbit model for the spectra of nilpotent Gelfand pairs (p. 108)


13:30 Asilata Bapat (Australian National University)Recollement of perverse sheaves on real hyperplane arrangements (p. 106)

14:00 Thomas Gobet (The University of Sydney)A Soergel-like category for complex reflection groups of rank one (p. 107)

14:30 Valentin Buciumas (The University of Queensland)Quantum polynomial functors (p. 106)

49

Abstracts

1. Plenary 53

Special Sessions2. Algebra 563. Applied and Industrial Mathematics 604. Category Theory 645. Computational Mathematics 666. Differential Geometry 697. Dynamical Systems and Ergodic Theory 728. Functional Analysis, Operator Algebra, Non-commutative Geometry 749. Geometric Analysis 78

10. Geometry and Topology 8011. Harmonic Analysis 8312. Integrable Systems 8513. Mathematical Biology 8714. Mathematics Education 8915. Mathematical Physics 9316. Number Theory 9517. Optimisation 9718. Probability Theory and Stochastic Processes 10219. Representation Theory 106

51

1. Plenary

1.1. How to find non-trivial solutions out of trivialones

Renato Ghini Bettiol (City University of New York)

12:00 Thu 6 December 2018 – Braggs

A/Prof Renato Ghini Bettiol

Bifurcation Theory originates from problems inApplied Sciences and Engineering (such as thebuckling of columns under compressive stress), andwas developed by mathematicians into a power-ful toolkit that uses the instability of solutions tocertain problems to prove the existence of othersolutions nearby. These “bifurcating” solutions areoften less symmetric and harder to find directly,but can provide very interesting examples. In thistalk, I will give a broad overview of topologicalbifurcation methods with plenty of examples, start-ing from Undergraduate Calculus, moving into Par-tial Differential Equations, and then finally somerecent applications in Geometric Analysis.

1.2. Maximal Monotonicity versus Convexity: Afruitful interplay

Regina Burachik (University of South Australia)


Regina Burachik

Perhaps the most important connection betweenmaximal monotone operators and convex functionsis the fact that the subdifferential of a convexfunction is maximal monotone (a result establishedby Rockafellar in 1970). This connection defines amap from the set of convex functions to the set ofmaximal monotone operators.

The focus of my talk is to describe maps travel-ing in the opposite direction. Namely, to a givenmaximal monotone operator T , we will associate afamily of convex functions, denoted by H(T ). Forachieving this, I will recall a family of so-called“enlargements” of T (i.e., point-to-set maps whosegraph contains the graph of T ), denoted by E(T ).The elements of E(T ) enjoy better continuity prop-erties than T itself, and it is, therefore, useful fordefining approximations of inclusion problems in-volving T . As a recent application of the familyH(T ) of convex functions, I will define a newlyintroduced concept of distance between two point-to-set maps, one of them being maximal monotone.This distance is inspired by the now well-knownconcept of Bregman distance, which, in turn, isoriginally induced by a convex function. Hence,this new concept of distance provides a furtherexample of the fruitful two-way interplay betweenmaximal monotone operators and convex func-tions.

1.3. Numerical methods for partial differentialequations with random coefficients

Josef Dick (University of New South Wales)

10:30 Fri 7 December 2018 – Braggs

Assoc Prof Josef Dick

Mathematical models often contain uncertainty inparameters and measurements. In this talk wefocus on partial differential equations where someparameters are modeled by random variables. Themain example comes for the diffusion equationwhere the diffusion parameters is modeled as arandom field which randomly fluctuates around agiven mean. We discuss recent progress on numer-ical methods in quantifying this uncertainty.

1.4. The topology of real analytic curves in theplane

Etienne Ghys (Ecole normale superieure de Lyon)


Prof Etienne Ghys

In the neighborhood of a singular point, a realanalytic curve in the plane consists of a finite num-ber of branches. Each of these branches intersectsa small circle around the singular point in twopoints. Therefore, the local topology is describedby a chord diagram: an even number of pointson a circle paired two by two. Not all chord di-agrams come from a singular point. The mainpurpose of this talk is to give an complete descrip-tion of those “analytic” chord diagrams. On ourway, we shall meet some interesting concepts fromcomputer science, graph theory and operads.

1.5. Nodal sets of eigenfunctions of the Laplacian,with randomness

Manjunath Krishnapur (Indian Institute of Science

Bangalore)

11:00 Wed 5 December 2018 – Braggs

Prof Manjunath Krishnapur

There has been a long study of nodal sets (zerolevel sets) of eigenfunctions of the Laplacian on aRiemannian manifold. Some questions of interestare about the length (or appropriate dimensionalHausdorff measure) of the nodal set, the numberof nodal domains, the topology of nodal domains,etc. Some of these questions are difficult and opento this day. Answers are sometimes easier andmore precise when one adds some randomness intothe problem. In this talk, we survey some recentresults in two settings of randomness:

1) For random linear combinations of eigenfunc-tions of the Laplacian on the 2-dimensional torus,the total length of the nodal set is a random vari-able whose variance has interesting dependence on

53

1. Plenary

the distribution of lattice points on circles. Thisis joint work with Igor Wigman and Par Kurlberg.We shall also mention extensions of this work, in-cluding central limit theorems for the nodal lengthby many other authors.

2) The sign of second eigenvector of the Laplacianof a weighted graph partitions the graph into twoparts. In the simplest case of a line graph endowedwith i.i.d. edge weights, we observed that if theedge-weights are supported away from 0, then thetwo parts are almost equal, but if the edge-weightscan be close to zero, then the smaller of the lengthscan be anywhere between 0 and 1/2. We explainthis observation. This is joint work with ArvindAyyer.

1.6. Just Enough Twisting

Joan Licata (Australian National University)


Dr Joan Licata

Low-dimensional contact geometry is the study oftwisting plane fields on 3-manifolds. We’ll startby making this notion precise, and then discusssome of the consequences and questions that arisenaturally from equipping topological objects withthis extra geometric structure. The second halfof the talk will focus on the surprising differencesbetween plane fields that twist “just enough” andthose that twist “too much” and examine the ex-tent to which this twisting can be localized.

1.7. Near-criticality in mathematical models ofepidemics

Malwina Luczak (The University of Melbourne)

12:00 Tue 4 December 2018 – Braggs

Prof Malwina Luczak

In an epidemic model, the basic reproduction num-ber R0 is a function of the parameters (such asinfection rate) measuring disease infectivity. In alarge population, if R0 > 1, then the disease canspread and infect much of the population (super-critical epidemic); if R0 < 1, then the disease willdie out quickly (subcritical epidemic), with onlyfew individuals infected.

For many epidemics, the dynamics are such thatR0 can cross the threshold from supercritical tosubcritical (for instance, due to control measuressuch as vaccination) or from subcritical to super-critical (for instance, due to a virus mutation mak-ing it easier for it to infect hosts). Therefore,near-criticality can be thought of as a paradigmfor disease emergence and eradication, and under-standing near-critical phenomena is a key epidemi-ological challenge.

In this talk, we explore near-criticality in the con-text of some simple models of SIS (susceptible-infective-susceptible) epidemics in large homoge-neous populations.

1.8. Robust chaos: a tale of blenders, theircomputation, and their destruction

Hinke Osinga (The University of Auckland)


Prof Hinke Osinga

A blender is an intricate geometric structure of athree- or higher-dimensional diffeomorphism. Itscharacterising feature is that its invariant mani-folds behave as geometric objects of a dimensionthat is larger than expected from the dimensionsof the manifolds themselves. We introduce a fam-ily of three-dimensional Hnon-like maps and studyhow it gives rise to an explicit example of a blender.The map has two saddle fixed points. Their as-sociated stable and unstable manifolds consist ofpoints for which the sequence of images or pre-images converges to one of the saddle points; suchpoints lie on curves or surfaces, depending on thenumber of stable eigenvalues of the Jacobian atthe saddle points. We employ advanced numericaltechniques to compute one-dimensional stable andunstable manifolds to very considerable arclengths.In this way, we not only present the first images ofan actual blender but also obtain a convincing nu-merical test for the blender property. This allowsus to present strong numerical evidence for theexistence of the blender over a larger parameterrange, as well as its disappearance and geometricproperties beyond this range. We will also discussthe relevance of the blender property for chaoticattractors.

This is joint work with Stephanie Hittmeyer andBernd Krauskopf (University of Auckland) andKatsutoshi Shinohara (Hitotsubashi University).

1.9. Analysis in non-smooth spaces using paths

Nageswari Shanmugalingam (University of

Cincinnati)

11:30 Fri 7 December 2018 – Braggs

Prof Nageswari Shanmugalingam

Classical analysis on Riemannian manifolds as-sumes the vector space structure (tangent spaces),with each point in the manifold equipped with avector space. Calculus on mappings on the mani-fold is done by restricting the function to curves inthe manifold with a prescribed tangent at the basepoint in the manifold. In generally non-smoothmetric spaces, where no tangent space structure,this approach can still be fruitful, leading to the no-tion of upper gradients first proposed by Heinonenand Koskela in the 1990s. The goal of this talk isto give a general overview of first order calculus

54

1. Plenary

on metric measure spaces developed in the pasttwenty years using this notion of upper gradients.

1.10. Recent Advances in Climate Sensitivity

Steven Sherwood (University of New South Wales)


Prof Steven Sherwood

The “climate sensitivity” S is defined as the equi-librium warming of the Earth when subjected toa doubling of its atmosphere’s carbon dioxide con-centration. Estimates of this core parameter ofEarth’s climate have ranged from 1.5–4.5 ◦C sincethe first credible attempts to quantify it in the1960s. The width and location of the pdf of Shave large implications for future global warming,mitigation, and adaptation. We now have multiplelines of evidence that provide information on S,though no line of evidence can provide a preciseestimate on its own. Past climate assessments, inparticular those of the Intergovernmental Panelon Climate Change (IPCC), have provided con-fidence intervals on S based on expert judgment.In this talk I will discuss the first attempt by theclimate community to quantify a posterior pdf ofS using Bayesian methodology that takes into ac-count the full range of evidence. The effort hasraised a number of interesting issues around themeaning and interpretation of priors and modeland error independence, but reveals the power andimportance of Bayesian inference — and leads toan interesting result.

1.11. A mathematical journey into nanoscience andnanotechnology

Natalie Thamwattana (The University of Newcastle)


Prof Natalie Thamwattana

Applying mathematics in nanoscience and nan-otechnology forms a modern area of research whereanalytical and computational tools in mathemat-ical sciences solve a wide range of problems innanoscience and nanotechnology. Mathematicalmodelling generates important new insights intocomplex processes and reveals optimal parametersand situations that might otherwise be difficult orcostly to obtain, especially through experimenta-tion. This talk will focus on modelling the interac-tions between nanostructures and applications ofthese structures in energy, biology and medicine.Join me on a magical journey into the nanoscalewhere beautiful mathematics finds fascinating newapplications.

1.12. Semi-simplicity in representation theory

Geordie Williamson (The University of Sydney)


Prof Geordie Williamson

Representation theory is the study of linear sym-metry. Since the first papers on the representationtheory of finite groups by Frobenius at the end ofthe 19th century, the theory has grown to forma fundamental tool of modern pure mathematics,with applications ranging from the standard modelin particle physics to the Langlands program innumber theory. Some of the most important the-orems in representation theory assert some formof semi-simplicity. Examples include Maschke’stheorem on representations of finite groups overthe complex numbers (proved in 1897), Weyl’stheorem on representations of compact Lie groups(proved in 1930), and the Kazhdan-Lusztig conjec-ture (proved by Beilinson-Bernstein and Brylinski-Kashiwara in 1980). This talk will be an intro-duction to these ideas, with an emphasis on ourattempts to uncover further layers of hidden semi-simplicity.

55

2. Algebra

2.1. Linear codes from matrices: answering aquestion of Glasby and Praeger

Faezeh Alizadehs (Shahid Rajaee Teacher Training

University)

17:30 Wed 5 December 2018 – Horace Lamb

Faezeh Alizadeh, Cheryl Praeger, Stephen Glasby

Let F be a field and let F r×s denote the spaceof r × s matrices over F . Let K be an extensionfield of F . Given matrices A in Kr×r and B inKs×s we call the subspace CF (A,B) := {X ∈F r×s|AX = XB} an intertwining code. Let R, kand d be rate, dimension and minimum distanceof CF (A,B), respectively. In the paper [1] the au-thors asked whether there is a sequence C1, C2, . . .of intertwining codes over a field F with parame-ters [risi, ki, di] for which the quantity Ridi = kidi

risiapproach infinity. In this talk I will answer thequestion affirmatively. Finally, a sequence of inter-twining codes with large minimum distance whenthe field is small was constructed.

2.2. On von Neumann regularity of simple flatLeavitt path algebras

Ambily Ambattu Asokan (Cochin University of

Science and Technology)


Dr Ambily Ambattu Asokan

In this talk, we shall discuss an open questionthat whether the flatness of simple modules overa unital ring implies all modules are flat and thusthe ring is von Neumann regular. This questionwas asked by Ramamurthi over 40 years ago. Hecalled such rings SF-rings. We shall discuss the vonNeumann regularity of SF Leavitt path algebras.

This is a joint work with Roozbeh Hazrat andHuanhuan Li.

2.3. Formal languages in group co-word problems

Alex Bishops (University of Technology, Sydney)


Alex Bishop

The co-word problem for a group, asks if a givenword does not represent the identity of the group.The interesting question is to classify classes ofgroups in terms of the complexity of their co-wordproblems; for example, a group has a co-wordproblem given by a regular language if and onlyif it is finite; or by a deterministic context-freelanguage if and only if it is virtually free.

In this talk, we will discuss groups with co-wordproblems given by a more exotic class of formallanguage known as ET0L which has recently gainedpopularity within areas of group theory. Thistalk will conclude with some interesting related

questions and some applications of ET0L in grouptheory.

2.4. Spaces at infinity for hyperbolic totallydisconnected locally compact groups

Timothy Peter Bywaterss (The University of

Sydney)

15:30 Tue 4 December 2018 – Horace Lamb

Mr Timothy Peter Bywaters

Totally disconnected locally compact (t.d.l.c.)groups which are generated by a compact set admita transitive action on a locally finite graph withcompact open vertex stabilisers. Such a graph isa generalisation of Cayely graph. Definitions suchas hyperbolic groups and their Gromov boundaryextend naturally to the non-discrete case.

T.d.l.c. groups also admit an action on a metricspace known as the space of directions. This spaceis an analogue of the Tits boundary for a nega-tively curved group and is effective at detectingfree abelian subgroups.

In my talk I will expand on both the Gromovboundary and space of directions for a hyperbolict.d.l.c. group and state a theorem relating them.

2.5. Lattice paths and submonoids of Z2

James East (Western Sydney University)


Dr James East

The study of lattice paths is a cornerstone of enu-merative combinatorics, and important applica-tions exist in almost all areas of mathematics. Thesubject goes back at least to the likes of Fermatand Pascal in the 1600s, and leads to many famousnumber sequences and arrays, including Fibonacci,Catalan, Motzkin, Delannoy and Schroder num-bers. The basic idea is to take some set X ⊆ Z2;see which points from Z2 you can get to by takinga “walk” from some designated origin using “steps”from X; and for each such point, calculate the to-tal number of such walks (which might be infinite).Sometimes constraints are also imposed, so thatthe walks must stay within a specified region ofthe plane (e.g., the first quadrant).

In this talk I’ll discuss some recent joint work withNicholas Ham, in which we take a kind of meta-approach to such problems, classifying the step setsfor which the solutions have various properties. Itturns out that finiteness properties of solutionsare closely related to the geometrical propertiesof the step set, algebraic properties of the monoidof endpoints, and combinatorial properties of cer-tain bi-labelled digraphs. There is an intriguingdivergence between the cases of finite and infinite

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2. Algebra

step sets, and some constructions rely on highlynon-trivial properties of real numbers.

2.6. Hausdorff dimension and normal subgroups offree-like pro-p groups

Alejandra Garrido (The University of Newcastle)


Dr Alejandra Garrido

Hausdorff dimension has become a standard tool tomeasure the size of fractals in real space. However,it can be defined on any metric space and thereforecan be used to measure the size of subgroups of,say, pro-p groups (with respect to a chosen metric).This line of investigation was started 20 years agoby Barnea and Shalev, who showed that p-adic an-alytic groups do not have any “fractal” subgroups,and asked whether this characterises them amongfinitely generated pro-p groups.

I will explain what all of this means and reporton joint work with Oihana Garaialde and Ben-jamin Klopsch in which, while trying to solve thisproblem, we ended up showing an analogue of atheorem of Schreier in the context of pro-p groupsof positive rank gradient: any finitely generated in-finite normal subgroup of a pro-p group of positiverank gradient is of finite index. I will also explainwhat “positive rank gradient” means, and whypro-p groups with such a property are “free-like”.

2.7. Algebraic K-theory, endomorphisms, and Wittvectors

David Gepner (The University of Melbourne)

13:30 Fri 7 December 2018 – Horace Lamb

Dr David Gepner

Algebraic K-theory is a deep and difficult invari-ant of algebraic objects such as ring and varietieswith numerous applications to number theory andgeometry. We will begin with an introduction toalgebraic K-theory and various related functors,such as Hochschild homology and cyclic homology.By a theorem of Almkvist, the endomorphism K-theory of a commutative ring is closely related toits ring of Witt vectors: more precisely, it containsthe ring of rational Witt vectors (a dense subringof all Witt vectors) as a summand. In addition tothe usual Witt vector operations, such as Frobe-nius and Verschiebung, we shall see that algebraicK-theory allows us to classify all suitably naturaloperations on the rational Witt vectors, answeringa question originally posed by Almkvist in the 70s.Portions of this talk will report on joint work withAndrew Blumberg and Goncalo Tabuada.

2.8. Subgroups of classical groups that aretransitive on subspaces

Michael Giudici (The University of Western

Australia)


Prof Michael Giudici

Let V be an n-dimensional vector space over thefinite field GF(q). There has been considerableinterest in subgroups of ΓLn(q) that are transitiveon the set of all k-dimensional subspaces of V , forsome k. For example, when k = 1 the classificationof all such subgroups enabled the classification ofall finite 2-transitive groups of affine type. Supposenow that V admits a nondegenerate sesquilinearor quadratic form and let G be the semisimilaritygroup of the form, that is G is a unitary, symplec-tic or orthogonal group. By Witt’s Lemma, G istransitive on the set U of k-dimensional subspacesof V of a given isometry type. Especially interest-ing are the cases where U is an orbit on totallysingular, or nondegenerate subspaces. In this talkI will discuss recent work with Stephen Glasbyand Cheryl Praeger that is looking to classify allsubgroups H of G that are transitive on U . Manyinteresting examples arise.

2.9. Permutations with orders coprime to a giveninteger

Stephen Glasby (The University of Western

Australia)


Dr Stephen Glasby

Erdos and Turan, in 1967, showed that the pro-portion of permutations in the symmetric groupSym(n) of degree n with no cycle of length divis-

ible by a fixed prime m is Γ(1 − 1m )−1

(nm

)− 1m +

O(n−1− 1m ). Let m be a positive square-free integer

and let ρ(m,n) be the proportion of permutationsof Sym(n) whose order is coprime to m. We showthat there exists a positive constant C(m) suchthat

C(m)(nm

)φ(m)m −1

6 ρ(n,m) 6(nm

)φ(m)m −1

for all n > m,

where φ is Euler’s totient function.

The motivation for this problem arose from com-putational group theory, and I will mention somerelevant classical results in statistical group theoryto place our work in context. This is joint workwith John Bamberg, Scott Harper, and Cheryl E.Praeger.

2.10. Finite simple images of finitely presentedgroups

Carlisle King (The University of Western Australia)


Dr Carlisle King

57

2. Algebra

Given a finitely presented group Γ, one can askwhich finite simple groups are images of Γ. Thereis a large literature on the study of finite imagesof various families of finitely presented groups aris-ing geometrically, such as Fuchsian groups andhyperbolic groups. We will study a new result inthis area concerning the free product Γ = A ∗ Bof nontrivial finite groups A and B, proved usingprobabilistic methods.

2.11. Koszul and Cohen-Macaulay properties ofresidual intersections

Neeraj Kumars (IIT Bombay)

10:00 Thu 6 December 2018 – Horace Lamb

Dr Neeraj Kumar

The notion of residual intersection was introducedby Artin and Nagata. In this talk, we shall seeKoszul and Cohen-Macaulay properties of diag-onal subalgebras of bigraded geometric residualintersections. Given a perfect ideal of height twoin a polynomial ring, we show that all their pow-ers have a linear resolution, and we shall discussthe Koszul, and Cohen-Macaulay property of thediagonal subalgebras of their Rees algebras. Thisis a joint work with H. Ananthnarayan and VivekMukundan.

2.12. On Kurosh-Amitsur and base radical classesfor a non-associative setting

Robert McDougall (University of the Sunshine

Coast)


Dr Robert McDougall

In this presentation we give a complete listing ofthe radical and semisimple classes for both Kurosh-Amitsur (KA) and base radical constructions in auniversal class generated by a non-associative ring.We identify classes that are radical or semisimpleunder one construction but not the other.

2.13. Locally compact piecewise full groups

David Robertson (The University of Newcastle)


Mr David Robertson

A group G acting faithfully by homeomorphisms ofthe Cantor set is called piecewise full if any home-omorphism assembled piecewise from elements ofG is itself an element of G. I will discuss whensuch a group admits a non-discrete locally compactsecond countable group topology and describe anumber of examples. This is joint work with Ale-jandra Garrido and Colin Reid.

2.14. What is a partial semigroup?

Tim Stokes (University of Waikato)


Dr Tim Stokes

Free algebras make sense for any sufficiently well-behaved class of algebras of some fixed type. Thereis interest in extending the idea to partial alge-bras. For example, there is a useful notion of freecategory in which the free objects are built fromdirected graphs rather than sets. Categories arepartial semigroups, and in thinking about how toextend the notion of freeness to partial semigroupsin general, one must first decide what “partialsemigroup” means. In this talk we explore variouspossible definitions and how they relate, givingexamples. We then return to what the free objectslook like: of course, this depends which definitionone uses.

This is joint work with Professor Victoria Gould(York University, UK).

2.15. Markov association schemes

Jeremy Sumner (University of Tasmania)


Dr Jeremy Sumner

I will discuss what is a compelling example of themathematics of phylogenetics leading to a novelalgebraic structure. The motivation for this workcomes from a simple model of aminoacyl-tRNAsynthetase (aaRS) evolution devised by Julia Shore(UTAS) and Peter Wills (U Auckland). Startingwith a proposed rooted tree describing the special-ization of aaRS through evolution of the geneticcode, their model produces a space of Markov ratematrices that form a commutative algebra undermatrix multiplication. We refer to each of theseas a ‘tree-algebra’.

By their construction, one initially expects that thetree-algebras occur as an instance of associationschemes. However this is not the case, and furtherstudy has revealed that both the tree-algebras andassociation schemes occur as a special case of amore general (and plausibly novel) algebraic struc-ture which we have coined ‘Markov associationschemes’.

I will describe our first steps in attempting to char-acterize the Markov association schemes. In par-ticular presenting two binary operations of ‘sum’and ‘product’ on the class of the schemes.

2.16. Some results differentiating Kurosh-Amitsurand base radical classes

Lauren Thorntons (University of the Sunshine

Coast)


Miss Lauren Thornton

58

2. Algebra

It is known that Kurosh-Amitsur (KA) and baseradical classes coincide in the universal class ofassociative rings but that not all KA radical classesare base radical in a more general setting. Inthis presentation we offer up some results whichcompare and contrast the two constructions toreveal a “hybrid” object that is both radical andsemisimple but not necessarily both KA-radicaland KA-semisimple.

2.17. Totally disconnected, locally compact groupsfrom transcendental field extensions

Stephan Tornier (The University of Newcastle)


Dr Stephan Tornier

(Joint work with Timothy P. Bywaters) Let Eover K be a field extension. Then the group ofautomorphisms of E which pointwise fix K is totallydisconnected Hausdorff when equipped with thepermutation topology. We study examples, aimingto establish criteria for this group to be locallycompact, non-discrete and compactly generated.

2.18. Solvable locally compact contraction groupsare nilpotent

George Willis (The University of Newcastle)


Prof George Willis

If G is a connected Lie group with an automor-phism, α, such that αn(x)→ 1 as n→∞ for everyx ∈ G, then G is nilpotent. This fact, which iswell-known, may be proved by passing to the Liealgebra of G and using elementary linear algebra.

The corresponding statement does not hold in fullgenerality when G is totally disconnected and lo-cally compact, as examples built from non-abelianfinite simple groups show. It does hold if G is solv-able however. The argument falls into two cases,since G is the direct sum of closed subgroups

G = D ⊕ Twith D divisible and T torsion. The divisible fac-tor D may be shown, using work of Lazard, to bethe direct sum of p-adic analytic groups and thesemay be shown to nilpotent by the same argumentusing the Lie algebra. The torsion case requires amore direct argument.

This is joint work with Helge Glockner.

2.19. Coxeter Systems for which the Brink-Howlettautomaton is minimal

Yeeka Yaus (The University of Sydney)


James Parkinson and Yee Yau

In their celebrated 1993 paper, Brink and Howlettproved that all finitely generated Coxeter groupsare automatic. In particular, they constructed a

finite state automaton recognising the language ofreduced words in a Coxeter group. This automatonis not minimal in general, and recently ChristopheHohlweg, Philippe Nadeau and Nathan Williamsstated a conjectural criteria for the minimality. Inthis talk we will explain these concepts, and provethe conjecture of Hohlweg, Nadeau, and Williams.This work is joint with James Parkinson.

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3.1. Choosing investment frequency to minimisebrokerage costs

Kieran Clancy (Flinders University)

17:00 Wed 5 December 2018 – Ligert 316

Dr Kieran Clancy

We consider a practical and seemingly simple prob-lem in financial mathematics: Suppose that Joesets aside $100 every week to invest in some shares.He predicts that the shares will have a rate ofreturn of 8% per annum, while his bank interestis just 3% per annum. Joe would prefer to buythe shares immediately, but every time he buys aparcel of shares he has to pay a brokerage of $10,regardless of the amount purchased. Is it betterfor Joe to accumulate his savings for a numberof weeks before purchasing the shares? If so, howlong should Joe save up before buying each par-cel? This problem is generalised and a solutionis presented including a closed-form approxima-tion using a Taylor series expansion. This talk issuitable for undergraduate audiences.

3.2. Mathematical problems of long wavetransformation in a coastal zone with a variablebathymetry

Andrei Ermakovs (University of Southern

Queensland)

14:00 Tue 4 December 2018 – Ligert 316

A.M. Ermakov, and Y.A. Stepanyants

We apply the rigorous mathematical methods toinvestigate surface wave transformation in a basinwith a variable bathymetry. The development ofrigorous mathematical methods for the descrip-tion of wave transformation in the coastal zonerepresents an important and topical problem bothfrom the academic and practical points of view,especially in the application of the protection ofthe Australian coastline from the hazardous im-pacts of oceanic waves. We consider long linearwave transformations in a coastal zone where waterdepth can vary arbitrarily smoothly. The derivedsystem of differential equations that describes thechanges of wave speed and free surface elevationare solved exactly for the different types of bottomprofile. New analytical solutions in terms of specialfunctions for wave transformation were obtained.The transformation coefficients were derived as thefunctions of wave frequency and the total depthdrop for three typical models: piece-linear, piece-quadratic, and hyperbolic tangential depth profiles.For all these cases we have derived exactly solvableequations and obtained their solutions in termsof hypergeometric functions. The influence of thegoverning parameters on the type of wave trans-formation was analysed. We show that the results

obtained are in agreement with the energy fluxconservation and Lamb’s formula in the limitingcase of zero frequency.

3.3. Optimal scheduling of trains using connecteddriver advice system

Ajini Galapitages (University of South Australia)


Mrs Ajini Galapitage

On most railways, if a train is delayed then fol-lowing train get to know about the delay whenthe driver saw a trackside signal. Then it willhave to slow significantly, which causes delays topropagate back along the track. By using in-cabDriver Advice Systems connected to centralisedscheduling systems, train delays can be detected asthey happen, and new schedules can be calculatedand issued to following trains so that additionaldelays are avoided.

The Scheduling and Control Group at the Univer-sity of South Australia and Sydney-based Com-pany TTG Transportation Technology have devel-oped the Energymiser Driver Advice System thatis used by train drivers to help them stay on timeand reduce energy use.

On large congested rail networks with many trains,such as passenger networks in Sydney, or the coalnetwork in the Hunter Valley, it is impossible toschedule the whole rail network at once in real timeas the problem is too large. An alternative, morepractical approach is to independently optimisesmall sections of the network, such as individuallines or junctions.

In this talk, I will present our methods to solve thejunction scheduling problem and line schedulingproblem with simulated examples in UK.

3.4. Population dynamics in a variable environment

Zlatko Jovanoski (University of New South Wales

Canberra)


Dr Zlatko Jovanoski

Many ecosystems are subject to external pertur-bations such as pollution, land clearing and sud-den shocks to their environment. However, mostcurrent models used do not take the changingenvironment into consideration. In cases wherethe changes in the environment are taken intoaccount this is usually done by specifying sometime-dependent function for the carrying capacitythat reflects the observed behaviour of the chang-ing environment.

Recent models developed by our group directlycouple the dynamics of one or two species with

60


their environments. This is achieved by treatingthe carrying capacity, a proxy for the state of theenvironment, as a state variable in the governingequations of the model. Thereby, any changes tothe environment can be naturally reflected in thesurvival, movement and competition of the specieswithin the ecosystem.

Furthermore, a vast majority of models are deter-ministic and cannot adequately account for randomexternal perturbation such as fires, drought, floods,contamination of water resources etc. By addingstochasticity (noise), it is possible to account forthese anomalous impacts on population dynamicsthat deterministic models often ignore.

For this talk a simple ecosystem consisting of asingle species and its variable environment is pro-posed. Specifically, a logistic population modelthat incorporates a stochastic carrying capacity isinvestigated. The carrying capacity is treated as astate variable and is described by a stochastic dif-ferential equation. The statistical properties of thecarrying capacity and the population are analysed.The probability distribution of the mean-time toextinction, the expected time evolution of the pop-ulation and its variance are computed using theMonte Carlo method.

3.5. About outlier detection

Sevvandi Priyanvada Kandanaarachchi (Monash

University)


Dr Sevvandi Priyanvada Kandanaarachchi

Does normalizing your data affect outlier detec-tion? It is common practice to normalize data be-fore using an outlier detection method. But whichmethod should we use to normalize the data? Doesit matter? The short answer is yes, it does. Thechoice of normalization method may increase ordecrease the effectiveness of an outlier detectionmethod on a given dataset.

In addition to normalization, what is the outlierdetection method best suited for my problem?Given an outlier detection problem, a suitableoutlier method is needed because the strengthsand weaknesses of methods are different, renderingeach method useful for a different set of prob-lems. Therefore, choosing a suitable normalizationmethod as well as an outlier detection method isimportant if one were to maximize performance.In this talk, we investigate this two-fold selectionusing meta-features of datasets and visualize therelative strengths and weaknesses of outlier meth-ods using instance space analysis.

3.6. Modelling Dye-Sensitized Solar Cells byNonlinear Diffusion

Benjamin Maldons (The University of Newcastle)

09:00 Thu 6 December 2018 – Ligert 316

Mr Benjamin Maldon

Dye-Sensitized Solar Cells (DSSCs) maintain highresearch interest, owing to their potential as aviable solution to the renewable energy problem.

While ample nanomaterials have been suggestedto improve their efficiency, mathematical mod-elling and analysis remains noticeably sparse. Thedominant model in this area remains the electrondiffusion equation, which has been extended toinclude time-dependence and nonlinear character-istics since its introduction 24 years ago.

In this talk, we analyse this diffusion equation byLie Symmetry and Homotopy methods and com-pare results to standard finite difference numericalsolutions to obtain the characteristic traits of aDSSC.

3.7. MMM, microwaves measure moisture

Mark Joseph McGuinness (Victoria University of

Wellington)


Prof Mark Joseph McGuinness

Measure the moisture content of bauxite in realtime on a conveyor belt as it is offloaded from a ship- this is the challenge that alumina company RusalAughinish brought to a European Study Groupwith Industry, held during one week in June 2017at the Univeristy of Limerick in Ireland. Rusalwere using a newly installed microwave analyser,and they sought our judgement on the reliability ofthe moisture measurements produced by the anal-yser. If you come to this talk, you will hear howwe tackled the data and information provided, andwhat we learned about the physics of microwavespropagating through a field of polarisers. Come,and be amazed at the twist and turns of our nego-tiations of the path to enlightenment.

3.8. No Jab, no pay

Mark Nelson (University of Wollongong)


Assoc Prof Mark Nelson

Before vaccination campaigns in the 1960s and1970s disease such as diphtheria, tetanus, andwhooping cough were responsible for killing thou-sands of children in Australia. Wide-spread vacci-nation programs have almost eliminated the deathof children from these disease in Australia.

Opponents to vaccination have existed for as longas vaccination itself. The anti-vaccination move-ment received a major boost in 1998 with thepublication of a, now discredited, study in theLancet which claimed that the mumps, measles

61


and rubella (MMR) vaccine was related to autism.The publication of this study has lead to an in-crease in the number of opponents to vaccination.

What is the possible effect of the anti-vaccinationmovement upon the spread of contagious disease?

To answer this question we combine the standardSIR model with vaccination for the spread of acontagious disease with a, slightly modified, SIRmodel for the spread of the anti-vaccination con-tagion. This leads to a system of nine differentialequations. We use this model to investigate howthe spread of the anti-vaccination contagion withina town increases the number of infections of aninfectious disease (assumed to be measles) over atwenty-year time frame.

This is joint work with Matthew Giffard, a second-year undergraduate student at the University ofWollongong.

3.9. Large Scale Kidney Exchange ProgrammeModels: Saving Lives with Integer Programming

William Erik Pettersson (University of Glasgow)


Dr William Erik Pettersson

For people with end stage kidney disease, the bestpossible outcome is a transplant from a livingdonor. However, finding someone willing to sharea kidney is not easy, and is made harder if thedonor also has to be medically compatible. A kid-ney exchange programme facilitates the donationof kidneys amongst a group of donors and patients,which helps to alleviate this medical requirement.A pool involving these donor-patient pairs can bemodelled as a graph, with arcs representing com-patible donations. The exact goal of such a modeldepends on various ethical, legal and logistical con-siderations, but a common theme is the finding ofa largest cardinality cycle packing in this graph.Integer programming is a common technique insuch programmes, and many different models havebeen investigated in the literature. We examine anumber of these models in the context of transna-tional kidney exchange programmes, scaling theinstance sizes upwards to account for larger poolsizes. In this context we discuss various optionsand parameters for modelling which improve theefficiency of these algorithms at larger scales, aswell as experimental data presenting how theseoptions impact upon existing models.

3.10. Insights from the persistent homologyanalysis of porous and granular materials

Vanessa Robins (Australian National University)


Dr Vanessa Robins

Persistent homology is an algebraic topological tooldeveloped for data analysis that measures changes

in topology of a filtration: a growing sequence ofspaces indexed by a single real parameter. It pro-duces invariants called the barcodes or persistencediagrams that are sets of intervals recording thebirth and death parameter values of each homol-ogy class in the filtration. When the filtrationparameter is a length-scale, persistence diagramsprovide a comprehensive description of geometricstructure over the given parameter range.

The physical properties of porous and granularmaterials critically depend on the topological andgeometric details of the material micro-structure.For example, the way water flows through sand-stone depends on the connectivity and diametersof its pores, and the balance of forces in a grain siloon the contacts between individual grains. Thesematerials are therefore a natural application areafor persistent homology.

My work with the x-ray micro-CT group at ANUhas produced topologically valid and efficient algo-rithms for studying and quantifying the intricatestructure of complex porous materials. Our codepackage, diamorse, for computing skeletons, parti-tions, and persistence diagrams from 2D and 3Dimages is available on GitHub. The code containsseveral optimisations that allow it to process im-ages with up to 20003 voxels on a high-end desktopPC. This software is enabling us to explore the con-nections between topology, geometry and physicalproperties of sandstone rock cores and granularpackings. We have shown that persistence dia-grams display a clear signal of crystallisation inbead packings, the degree of consolidation in sand-stones, percolating length scales in porous media,and the trapping of non-wetting phase in two-phasefluid flow experiments.

3.11. A coupled flow and temperature model forfibre drawing

Yvonne Stokes (The University of Adelaide)


Prof Yvonne Stokes

In the drawing of optical fibres viscosity is stronglytemperature dependent. Surprisingly, where otherparameters are assumed to be constant and onlythe final fibre geometry obtained from the initialpreform geometry is important, a flow model isall that is required. If, however, there is a desireto know the geometry along the neck-down lengthfrom preform to fibre, then a temperature modelmust be coupled to the flow model; likewise, ifparameters apart from the viscosity (e.g. surfacetension) are temperature dependent.

In this talk we outline the derivation of an efficientasymptotic model for the drawing of fibres witharbitrary cross-sectional geometry. ODEs describethe change in area of the cross-section and the tem-perature from preform to fibre. In general, these

62


are coupled with a 2D transverse-flow problemdescribing the evolution of the geometry in thecross-section due to surface tension and pressure.The accuracy of the model is demonstrated bycomparison with experiments and finite-elementsimulations.

3.12. ST-metric estimation of factor weights

Ilknur Tulunay (University of Technology, Sydney)


Dr Ilknur Tulunay

Consider discrete plane curves on (0, 1] x (0, 1].ST-metric can be thought as distances betweenthe discrete curves. It is defined as a square rootof the symmetrized relative entropy of two n-pointsets on (0, 1] and their averages. This idea hasbeen introduced and applied to the performancemeasures of portfolios by Tulunay (2017). Factoranalysis of major indexes are examined by Ang etal (2018) where the objective function of the opti-mization problem is set as tracking error (trackingdifferences times the standard deviation over someperiod). We purpose ST-metric optimization tofind the factor exposures (weights) for a given in-dex (or stock). Empirical evidence shows thatST-metric method gives better estimation of thefactor exposures (weights).

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4. Category Theory

4.1. Bicategories vs Rezk’s weak 2-categories

Alexander Campbell (Macquarie University)

09:00 Thu 6 December 2018 – Eng Math G06

Dr Alexander Campbell

For each n ≥ 0, Rezk defined a model structure onthe category of simplicial presheaves over Joyal’scategory Θn whose fibrant objects are a model forweak n-categories. In this talk, I will show that thismodel is equivalent in the cases n = 0, 1, 2 to theclassical notions of set, category, and bicategory, inthe sense that they form Quillen equivalent modelcategories. This is partly joint work with EdoardoLanari.

4.2. Analytic monads and infinity operads

David Gepner (The University of Melbourne)

16:00 Wed 5 December 2018 – Eng Math G06

Dr David Gepner

We develop an infinity-categorical version of theclassical theory of polynomial and analytic func-tors, initial algebras, and free monads. Using thismachinery, we provide a new model for infinity-operads as analytic monads. We justify this defi-nition by proving that the infinity-category of an-alytic monads is equivalent to that of dendroidalSegal spaces, which are known to be equivalent tothe other existing models for infinity-operads.

4.3. Inner horns for 2-quasi-categories

Yuki Maeharas (Macquarie University)

14:00 Tue 4 December 2018 – Eng Math G06

Mr Yuki Maehara

2-quasi-categories are a model for (∞, 2)-categories,defined as the fibrant Θ2-sets with respect to amodel structure due to Ara. Since this model struc-ture is constructed using Cisinski’s machinery, the2-quasi-categories and the fibrations between themcan be characterised by the right lifting propertywith respect to a certain set of maps that ad-mits an explicit description. However, this setis not very easy to work with from the combi-natorial viewpoint. In this talk, I will give analternative characterisation of (fibrations between)2-quasi-categories using a much more convenientset, namely the inner horn inclusions and equiva-lence extensions introduced by Oury in his PhDthesis.

4.4. A new class of coloured modular operads

Marcy Robertson (The University of Melbourne)


Dr Marcy Robertson

Modular operads, defined by Getzler-Kapronov inthe 90s, originally came up as a way to encodethe combinatorics of the Feynman transform. Thecoloured version, also called compact symmetricmulticategories, can be thought of as a generali-sation of a category in which arrows are replacedwith undirected spans which allow for “feedback.”It has been unclear (at least to the speaker) whatexactly these coloured modular operads are sup-posed to be. In this talk we give a partial answerarising from the study of certain combinatorial ob-jects that arise in virtual and welded knot theory.

4.5. The right cancellation property of the class ofinner anodyne maps

Danny Stevenson (The University of Adelaide)


Dr Danny Stevenson

Some proofs in quasi-category theory can be sim-plified by exploiting the fact that certain classes ofsimplicial maps satisfy what is sometimes calledthe right cancellation property. It is well-knownthat the class of left and right anodyne maps sat-isfy this property. It is less well-known that theclass of inner anodyne maps also satisfies this prop-erty. I will discuss both the proof of this fact andsome applications.

4.6. Infinity Cyclic Operads

Michelle Strumilas (The University of Melbourne)


Miss Michelle Strumila

Dendroidal sets are a useful way of modelling in-finity operads. We have defined a dendroidal setbased on the mapping class groups of surfaces.We then go on to show that it is not an infinityoperad, but a strict operad, via a theorem aboutdendroidal groupoids.

4.7. The slice filtration and spectral sequence

Ivo De Los Santos Vekemanss (Australian National

University)


Mr Ivo De Los Santos Vekemans

A Postnikov tower from classical algebraic topol-ogy is built via localisation functors from a filteredsequence of localising subcategories τ≥n each gen-erated by spheres Sk for k ≥ n. Similarly, in theequivariant setting slice towers are built via local-ising functors from the slice filtration of localisingsubcategories generated by suitable representationspheres. In this talk I will introduce the slice tower,show how it gives an interesting spectral sequence(by contrast, the spectral sequence of a Postnikov

64

4. Category Theory

tower is stable on the first page) and detail such acalculation.

4.8. Algebras in Braided Tensor categories andEmbedded surfaces

Dominic Weillers (Australian National University)


Mr Dominic Weiller

Given a monoidal category, the algebra objects,their bimodules and bimodule intertwiners forma bicategory. If we start with a braided tensorcategory (BTC), the braiding produces a monoidalproduct of algebras making the category of alge-bras, bimodules and intertwiners into a tricategorywith a single 0-morphism (also called a monoidalbicategory). Using the theory of surface diagramsfor Gray categories with duals, one expects to pro-duce an ‘extended TQFT of embedded surfaces’given a special Frobenius algebra in a BTC.

We will consider a non-extended version and seehow to obtain invariants of embedded surfacesup to isotopy by drawing ‘fine enough’ trivalentgraphs on a surface and choosing a special Frobe-nius algebra. Interesting examples must come fromnon-symmetrically braided categories as algebrasin symmetric tensor categories give boring invari-ants. For example, picking the E6 algebra in A11

(a non-symmetric BTC) we can distinguish theunlinked union of two tori from two concentricallynested tori.

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5.1. A combined GDM-ELLAM-MMOC (GEM)scheme for advection dominated PDEs

Hanz Martin Chengs (Monash University)


Hanz Martin Cheng, Jerome Droniou, Kim-Ngan Le

We propose a combination of the Eulerian La-grangian Localised Adjoint Method (ELLAM) andthe Modified Method of Characteristics (MMOC)for time-dependent advection-dominated PDEs.The combined scheme, so-called GEM scheme,takes advantages of both ELLAM scheme (massconservation) and MMOC scheme (easier compu-tations), while at the same time avoids their disad-vantages (respectively, harder tracking around theinjection regions, and loss of mass). We presenta precise analysis of mass conservation propertiesfor these three schemes and numerical results il-lustrating the advantages of the GEM scheme. Aconvergence result of the MMOC scheme, moti-vated by our previous work on the convergence ofELLAM schemes, is provided, which can be ex-tended to obtain the convergence of GEM scheme.

5.2. What the second Strang lemma and theAubin-Nitsche trick should be

Jerome Droniou (Monash University)


Assoc Prof Jerome Droniou

The second Strang lemma is widely considered, inthe finite element community, as the key to estab-lish error estimates for linear problems written invariational/weak form. It has however limitationsthat prevent its application to important meth-ods, such as Finite Volume methods, discontinuousGalerkin, Virtual Element Methods, Hybrid HighOrder schemes, etc. Some of these methods arewritten in “fully discrete form”: (some of) their un-knowns are not functions on the physical domainof interest.

In this talk, I will present a ‘third Strang lemma’that is applicable to any scheme, including thosein fully discrete form. The idea is to estimate,in a discrete energy norm (“H1-like”, for 2nd or-der elliptic equations), the difference between thesolution to the scheme and an interpolant of thecontinuous solution. This third Strang lemma issimpler to prove and use than the second Stranglemma, and defines a natural notion of consistencythat satisfies the Lax principle: ‘stability + con-sistency implies convergence’.

I will also discuss improved estimates in a weaker(“L2-like”) norm, by presenting an Aubin-Nitschetrick adapted to schemes in fully discrete form. Iwill show that the terms to estimate when using

this Aubin-Nitsche trick are extremely similar tothe ones already estimated when applying the thirdStrang lemma.

I will conclude by showing how these generic resultsyield new estimates for Finite Volume methods(and, time permitting, for discontinuous Galerkin).

5.3. Recovery based finite element method forfourth-order PDEs

Hailong Guo (The University of Melbourne)


Dr Hailong Guo

In this talk, a recovery based finite element methodfor biharmonic equations is constructed and an-alyzed. In our construction, the popular post-processing gradient recovery operators are used tocalculate approximately the second order partialderivatives of a continuous linear finite elementfunction which do not exist in traditional meaning.The proposed scheme is straightforward and simple.More importantly, it is shown that the numericalsolution of the proposed method converges to theexact one with optimal orders both under L2 anddiscrete H2 norms, while the recovered numericalgradient converges to the exact one with supercon-vergence order. Some novel properties of gradientrecovery operators are discovered in the analysis ofour method. In several numerical experiments, ourtheoretical findings are verified and a comparisonof the proposed method with the nonconformingMorley element and C0 interior penalty method isgiven.

5.4. Using a crossing minimisation heuristic to solvesome open problems

Michael Haythorpe (Flinders University)

13:30 Fri 7 December 2018 – Ligert 314

Dr Michael Haythorpe

My colleagues and I were recently successful indeveloping QuickCross, a robust and highly effi-cient heuristic for minimising crossings. In thistalk, I will discuss how we have been able to useQuickCross to attack some problems in crossingminimisation, including determining the crossingnumbers of some infinite families of graphs, andanswering (in both the positive and the negative)some open conjectures about minimal graphs withcertain crossing numbers. I will also discuss our re-cently completed comprehensive survey of graphswith known crossing numbers, the first of its kindin this highly active area of research.

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5.5. Numerical linear algebra and the solution ofsystems of polynomial equations

Markus Hegland (Australian National University)


Prof Markus Hegland

In my talk I will give a short review of numericalmethods for the solution of systems of polynomialequations. I will in particular focus on the role ofsparse linear matrix factorisation.

5.6. Stochastic Navier-Stokes equations on a thinspherical domain

Quoc Thong Le Gia (University of New South

Wales)


Dr Quoc Thong Le Gia

We consider the incompressible stochastic Navier-Stokes equations on a thin spherical domain alongwith free boundary conditions under a randomforcing. We show that the martingale solution ofthese equations converge to the martingale solu-tion of the stochastic Navier-Stokes equation ona sphere as the thickness converges to zero. Thisis a joint work with Gaurav Dhariwal (Vienna,Austria) and Zdzislaw Brzezniak (York, UK).

5.7. A second-order time stepping scheme forfractional diffusion problems

William McLean (University of New South Wales)


Assoc Prof William McLean

I will describe recent work with Jiwei Zhang (Bei-jing Computational Science Research Center) andHong-lin Liao (Nanjing University of Aeronauticsand Astronautics) on the stability and convergenceof the Alikhanov scheme for a fractional diffusionequation. We employ variable time steps to resolvethe initial singularity in the solution. Our analy-sis relies on a novel Gronwall inequality which inturn requires us to prove a delicate monotonicityproperty of the Alikhanov weights.

5.8. QuickCross - a crossing minimisation heuristicbased on vertex insertion

Alex Newcombes (Flinders University)


Mr Alex Newcombe

The crossing number of a graph is the minimumnumber of edge crossings in any drawing of thegraph into the plane. Computing the crossingnumber is NP-hard and thus heuristic methodsfor minimising crossings are currently of interest.This talk will introduce a heuristic method forminimising crossings which is based upon repeat-edly solving the so-called vertex insertion problem.This is in contrast to the current state-of-the-artcrossing minimisation heuristic, the Planarization

Method, which is based primarily on edge inser-tion techniques. We show that our approach issimilarly effective in terms of solution quality andexecution time, and is often superior for denseinstances. In particular, we discuss a highly effi-cient implementation of our heuristic, which wecall QuickCross, and which is available for use.Several design aspects of the implementation arealso discussed.

5.9. A review of some approximation schemes usedin FFTs on non-uniform grids

Garry Newsam (The University of Adelaide)


Dr Garry Newsam

One of the two main constructions that enablefast computation of the discrete Fourier transformon non-uniform grids approximates the associatedmatrix F as

F ≈P∑p=1

DpFNEp.

Here FN is the standard N × N FFT matrix,Dp, Ep are diagonal matrices, and P = O(| log ε|)where ε is the desired approximation accuracy.The entries of the diagonal matrices are the vec-tors up,vp in a rank-P approximation UV T to a

matrix F derived from F that has the form

Fm,n = e2πixmyn xm, yn ∈ [−1/2, 1/2]1 ≤ m,n ≤ N.

Originally the rank-P approximations were con-structed via a standard Taylor series expansion ofthe exponential about the origin; more recently,Ruiz-Antolin and Townsend [SIAM J. Sci. Com-put., 40(1), pp. A529-A547, 2018] have constructedmore efficient and numerically stable approxima-tions based on expanding the exponential kernel asa bivariate series of Chebychev polynomials. Thetalk will compare these two schemes with alterna-tive schemes based on expanding the exponentialkernel in a Fourier-Bessel series and as a sum ofprolate spheroidal wave functions, and benchmarkall against the optimal rank-P approximations ob-tainable from the singular value decomposition ofF .

5.10. Integrating semilinear parabolic differentialinclusions with one-sided Lipschitz nonlinearities

Janosch Rieger (Monash University)


Prof Dr Wolf-Juergen Beyn, Prof Dr Etienne

Emmrich, Dr Janosch Rieger

Semilinear parabolic differential inclusions withLipschitz nonlinearities and their numerical ap-proximations have been studied extensively in theliterature. The established techniques for prov-ing existence results and error estimates are based

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on projections that reduce the differential inclu-sion to a differential equation and rely on theLipschitz property. To obtain similar results fornon-Lipschitzian nonlinearities, we extend tech-niques for relaxed one-sided Lipschitz differentialinclusions in finite-dimensional spaces to parabolicinclusions in the setting of Gelfand triples.

5.11. Sparse Isotropic Regularization for SphericalHarmonic Representations of Random Fields on theSphere

Yuguang Wang (University of New South Wales)


Quoc T. Le Gia, Ian Sloan, Rob Womersley and Yu

Guang Wang

I will talk about sparse isotropic regularizationfor a random field on the unit sphere S2 in R3,where the field is expanded in terms of a sphericalharmonic basis. A key feature is that the normused in the regularization term, a hybrid of the`1 and `2-norms, is chosen so that the regulariza-tion preserves isotropy, in the sense that if theobserved random field is strongly isotropic then sotoo is the regularized field. The Pareto efficientfrontier is used to display the trade-off between thesparsity-inducing norm and the data discrepancyterm, in order to help in the choice of a suitableregularization parameter. A numerical example us-ing Cosmic Microwave Background (CMB) data isconsidered in detail. In particular, the numericalresults explore the trade-off between regulariza-tion and discrepancy, and show that substantialsparsity can be achieved along with small L2 error.

5.12. Using spherical t-designs and `q minimizationfor recovery of sparse signals on the sphere

Robert Womersley (University of New South Wales)


Xiaojun Chen and Robert Womersley

This paper considers the recovery of sparse signalson the sphere from their low order, potentiallynoisy, Fourier-Laplace coefficients. The approachuses spherical t-designs (sets of points on the spherefor which equal weight cubature is exact for allspherical polynomials of degree at most t) to for-mulate a constrained `q(0 < q ≤ 1) minimizationmodel. We show that well-conditioned sphericalt-designs and `q minimization have effective prop-erties for recovery of sparse signals on the sphere.A key role is played by the separation of the un-derlying point set on which the discrete signalresides. Numerical examples and a discussion ofsuper-resolution are provided.

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6.1. The Alekseevskii conjecture: Overview andopen questions

Romina Melisa Arroyo (University of Queensland)

14:30 Tue 4 December 2018 – BS Sth 2051

Dr Romina Melisa Arroyo

One of the most important open problems on Ein-stein homogeneous manifolds is the Alekseevskiiconjecture. This conjecture says that any con-nected homogeneous Einstein space of negativescalar curvature is diffeomorphic to a Euclideanspace.

In this talk we aim to discuss recent advancestowards the above mentioned conjecture, share ourcontributions and describe some open problems.

This talk is based in a joint work with RamiroLafuente (The University of Queensland).

6.2. A gluing formula for families Seiberg-Witteninvariants

David Baraglia (The University of Adelaide)

17:00 Wed 5 December 2018 – BS Sth 2051

Dr David Baraglia

The families Seiberg-Witten (SW) invariant is ageneralisation of the ordinary SW invariant tofamilies of smooth 4-manifolds. We use a gluingconstruction to study the SW equations on a fam-ily of connected sums. The result is a formulawhich allows the computation of certain familiesSW invariants in terms of ordinary SW invari-ants. Amongst the applications of this result isan obstruction to the existence of positive scalarcurvature metrics invariant under a given group ofdiffeomorphisms. This talk is based on joint workwith Hokuto Konno and Mathai Varghese.

6.3. Convex Algebraic Geometry of CurvatureOperators

Renato Ghini Bettiol (City University of New York)


Prof Renato Ghini Bettiol

In this talk, I will discuss a few properties of the setof algebraic curvature operators of n-dimensionalspaces satisfying a sectional curvature bound, un-der the light of the emerging field of Convex Alge-braic Geometry. This is a report on joint work (inprogress) with M. Kummer and R. Mendes.

6.4. Positive curvature in dimension 7

Owen Dearricott (The University of Melbourne)


Dr Owen Dearricott

In this talk I outline a construction for putting pos-itive sectional curvature on a series of 7-manifolds

discussed as viable candidates to carry positivelycurved metrics with co-dimension one principal or-bits discussed by Grove, Wilking and Ziller in JDGin 2008 by appropriately modifying a naturally oc-curring 3-Sasakian metric. This builds on previouswork where I considered isolated examples of thissort where the base Bianchi IX self-dual Einsteinorbifold metric had an algebraic closed form.

6.5. Three-dimensional Sasakian structures andpoint-extension of monopoles

Kumbu Dorjis (University of New England)


Mr Kumbu Dorji

Let M be a compact, oriented, Riemannian three-manifold, admitting a geodesible Killing vectorfield along which the Ricci curvature tensor is ev-erywhere positive, and is constant outside a com-pact subset K of M . Let E be a smooth complexvector bundle, defined initially over M \ {P}, withconnection ∇ and endomorphism ϕ satisfying themonopole equation on M \ {P}. In this talk weshow that M admits a local Sasakian structureoutside K. Moreover, assuming that all prescribedsingularities of the monopole field are contained inK, we use this structure together with methods ofcomplex analysis to provide sufficient conditionsfor smooth extension of the monopole across P .

6.6. The exceptional aerobatics of flying saucers

Michael Eastwood (The University of Adelaide)


Prof Michael Eastwood

The motion of a flying saucer is restricted by thethree-dimensional geometry of the space in whichit moves. In this way, various Lie algebras arisefrom thin air. I shall discuss the geometry of theparticular thin air needed so that Engel’s 1893construction of the exceptional Lie algebra G2emerges. This is joint work with Pawel Nurowski.

6.7. Scalar curvature and projectivecompactification

Keegan Floods (The University of Auckland)

09:00 Thu 6 December 2018 – BS Sth 2051

Mr Keegan Flood

In this talk we will use projective tractor calculusto study the geometry of solutions to the PDEgoverning the metrizability of projective manifolds.As a consequence we will see that under suitableassumptions on the (generalized) scalar curvature

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the “boundary at infinity” of a projectively com-pact pseudo-Riemannian metric inherits a well-behaved geometric structure from that of the in-terior. We will examine the non-vanishing scalarcurvature case which yields a conformal structureon boundary, then the scalar-flat case which yieldsa projective structure on the boundary.

6.8. Corners in C∞-Algebraic Geometry

Kelli Francis-Staites (The University of Oxford)


Miss Kelli Francis-Staite

The moduli spaces of J-holomorphic curves in asymplectic manifold can be used to define invari-ants of the manifold, such as the Gromov-Witteninvariants. The geometric structure on these mod-uli spaces used to define these invariants has severaldifferent models. These models include the Ku-ranishi spaces of Fukaya-Oh-Ohta-Ono, and thepolyfolds approach of Hoefer. There is now interestin using derived differential geometry to describethese moduli spaces, such as in the work of Joyce;the suggested geometric structure is a ‘d-orbifoldwith corners’.

To define such spaces, the theory of C∞-algebraicgeometry has been extended to include manifoldswith corners. This talk will present foundationalwork in this area. Specifically, we will consider C∞-schemes, a category that contains smooth mani-folds but also their fibre products, and how togeneralise this to manifolds with corners. This isjoint work with Joyce. If time, we will considerhow to recover the corners structure from these‘C∞-schemes with corners’.

6.9. Properties of some quasi-geodesics on Stiefelmanifolds

Krzysztof Krakowski (Cardinal Stefan Wyszynski

University in Warsaw)


Dr Krzysztof Krakowski

We consider a class of curves of constant curvatureon Stiefel manifolds called quasi-geodesics. Theyfind their applications in computer vision and pat-tern recognition, where they serve as interpolatingcurves. I will review geometric properties of quasi-geodesics on Stiefel manifolds and their connectionwith solutions of a sub-Riemannian optimal controlproblem on a Lie group that acts on the manifold.

6.10. Homogeneous Einstein manifolds via acohomogeneity-one approach

Ramiro Augusto Lafuente (The University of

Queensland)


Dr Ramiro Augusto Lafuente

We establish new non-existence results on non-compact homogeneous Einstein manifolds. Thekey idea of the proof is to consider non-transitivegroup actions on these spaces (more precisely, ac-tions with cohomogeneity one), and to find geo-metric monotone quantities for the ODE that re-sults from writing the Einstein equation in such asetting. As a first application, we show that homo-geneous Einstein metrics on Euclidean spaces areEinstein solvmanifolds. In addition, non-existenceof left-invariant Einstein metrics on the Lie groupSl(2,R)k also follows, and this is the first time thatthe Alekseevskii conjecture has been verified fora non-compact semisimple Lie group (in higherdimensions). This is joint work with C. Bohm.

6.11. An Information Geometric Approach ToPulse-Doppler Sensor Optimisation

Anthony Shane Marshalls (Flinders University)


Mr Anthony Shane Marshall

Information Geometry seeks to apply the methodsof Differential Geometry to the field of probabil-ity theory. The information geometric approachto the optimisation of radar systems provides aninteresting avenue for novel research, in an areawhere much practical and experimental knowledgealready exists. Investigating a Pulse-Doppler sen-sor system by this method involves describing acollection of sensors and a target, where any infini-tesimal variation in the configuration of the sensorsproduces a new information space, a point in the“Configuration Manifold”. The family of all config-uration metrics is then viewed as a sub-manifold ofthe manifold of all Riemannian metrics for the cor-responding state space. This is the set of all statesof the target, viewed as a Riemannian manifoldvia the information gain at a point in the space.Given some specific choice of sensor configuration,the determination of a geodesic path through the“information space” is then possible.An interestingfeature of this geodesic path is that by parametris-ing the geodesic by arc length, an optimal “speedlimit” for traversing the curve is obtained. The ex-istence of this speed limit is somewhat surprising,as it emerges naturally despite the fact that noequations of motion are included in the calculation.The system described above has, so far, only beeninvestigated for the 2D case with fixed sensor lo-cations and with the assumption that the sensorsand target “know” everything about each other.Systems of greater complexity are yet to be exam-ined. Further applications under investigation inthis research include the sonar employed by batsin their navigation and hunting. Bats have beenextensively studied and it is well known that theymodify their sonar “chirp” as they hunt. The ini-tial results of examining bat sonar reveals that the

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bats may be optimising information gain as theyreconfigure the parameters of their sonar system.

6.12. Signs for Real and equivariant gerbes

Michael Murray (The University of Adelaide)

14:00 Fri 7 December 2018 – BS Sth 2051

Prof Michael Murray

I will discuss how Real and equivariant gerbes ona manifold with involution give rise to signs overthe fixed points of the involution. In particularI’ll discuss the question of whether every possiblechoice of signs on the fixed points can arise froma Real or equivariant gerbe. These ideas have ap-plication to twisted K-theory although I probablywon’t have time to discuss that.

6.13. Nilpotent Lie groups and metric geometry

Alessandro Ottazzi (University of New South Wales)


Dr Alessandro Ottazzi

In this seminar I will consider some links betweenLie theory and metric geometry. For example, iftwo nilpotent Lie groups are isometric (with re-spect to some left-invariant distances) then theyare isomorphic (Kivioja, Le Donne 2017). However,if the two groups are only bi-Lipschitz equivalent(globally), then it is not known whether they areisomorphic. In fact, it is an important open prob-lem in geometric group theory to establish whetherquasi-isometric nilpotent Lie groups are isomor-phic. In the seminar I will discuss some results thatare related to this questions, obtained in differentcollaborations.

6.14. A criterion for local embeddability of3-dimensional CR-structures

Gerd Schmalz (University of New England)


Prof Gerd Schmalz

We introduce a CR-invariant class of Lorentzianmetrics on a circle bundle over a 3-dimensionalCR-structure, which we call FRT-metrics. Thesemetrics generalise the Fefferman metric, allowingfor more control of the Ricci curvature, but aremore special than the shearfree Lorentzian met-rics introduced by Robinson and Trautman. Ourmain result is a criterion for embaddability of 3-dimensional CR-structures in terms of the Riccicurvature of the FRT-metrics in the spirit of theresults by Lewandowski et al. and Hill et al. Thisis joint work with Masoud Ganji.

6.15. Distinguished curves in projective andconformal geometry

Daniel Snells (The University of Auckland)


Mr Daniel Snell

Distinguished curves play an important role inthe study of many geometries and are of interestfor a wide range of applications. Projective andconformal geometry are two examples of parabolicgeometries and thus possess natural notions of dis-tinguished curves.We will present a characterization of distinguishedcurves in these settings phrased in the languageof tractor calculus, a framework well suited to thestudy of parabolic geometries. We will also seehow this characterization may be used to produceconserved quantities along such curves.This is joint work with A. Rod Gover (Univer-sity of Auckland) and Arman Taghavi-Chabert(American University of Beirut).

6.16. Symmetry and Geometric Control Theory

Peter Vassiliou (Australian National University)


Dr Peter Vassiliou

An open question in geometric control theory isthat of explicit integrability. This is the prob-lem of characterizing those smooth nonlinear con-trol systems whose states and control inputs canbe parametrized by finite expressions of arbitraryfunctions and their derivatives. The control the-oretic notions of “differential flatness” and “dy-namic feedback linearization” constitute the cur-rent state of the art in this area. In this talk I willdescribe recent work that exploits an auspiciousclass of Lie group symmetries for this problem. Theproblem of constructing the required parametriza-tion is shown to be intimately associated to thegeometric properties of a certain principal connec-tion.

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7.1. Quasi-compactness and invariant measures forrandom dynamical systems of Jablonski maps

Fawwaz Bataynehs (University of Queensland)


Mr Fawwaz Batayneh

We define admissible random Jablonski maps andshow some results regarding the quasi-compactnessproperty and existence of absolutely continuousinvariant measures and physical measures. Illus-trative example will also be provided.

7.2. ‘Systems all the way down’: ManagingComplexity with BondGraphTools

Peter Cudmore (The University of Melbourne)


Dr Peter Cudmore

Many problems in biology, ecology and engineer-ing involve predicting and controlling complex sys-tems, loosely defined as interconnected system-of-systems. Such systems can exhibit a variety ofinteresting non-equilibrium features such as emer-gence, phase transitions and other multi-scale phe-nomenon which result from mutual interactionsbetween subsystems.

Constructing and analysing models of complex sys-tems is often a non-trivial task due to the highdimensionality, heterogeneity and nonlinearity ofthe system in question. Mathematicians and sci-entists alike need tools, computational tools inparticular, to manage the complexity of their dy-namical systems models.

In this talk we introduce ‘BondGraphTools’ a sys-tems modelling framework, and discuss how tomodel and simulate complex physical systems with-out making the models unwieldy, breaking the lawsof physics, or doing any of the tedious stuff byhand.

7.3. Lyapunov spectrum of Perron-Frobeniusoperator cocycles

Cecilia Gonzalez-Tokman (The University of

Queensland)


Dr Cecilia Gonzalez-Tokman

The Lyapunov spectrum of Perron-Frobenius cocy-cles contains relevant information about dynamicalproperties of random (non-autonomous) dynamicalsystems. Here, we describe the Lyapunov spectrumfor a family of expanding maps of the circle, anddiscuss natural perturbations which, in some pa-rameter regimes, induce collapse (instability) ofthis spectrum. This is joint work with AnthonyQuas.

7.4. Recent results in Thermodynamic Formalism

Renaud Leplaideur (Universite de la Nouvelle

Caledonie)


Mr Renaud Leplaideur

The goal of Dynamical System is to describe orbitsof the action. Due to chaos, it is usually impossi-ble to describe all the trajectories. The ErgodicTheorem allows to only describe almost all orbits.This “almost all ” makes reference to an invariant(probability) measure. The Thermodynamic For-malism is then a way to singularize one of thesemeasures, called equilibrium state. In this talk, oneshall present new developments in ThermodynamicFormalism.

Introduced in the 70s , mainly by Sinai, Ruelle andBowen, the theory holds for uniformly hyperbolicdynamical systems. Up to now, there is still nogeneral theory for the non-uniformly hyperbolicsystems. We shall present some recent results forthe case of Partially Hyperbolic Attractors withsingularities (as the Lorenz Attractor).

Thermodynamic Formalism was clearly inspired byStatistical Mechanics. However, despite the vocab-ulary is the same, the notions and the settings aresometimes different. We shall present here somerecent result on the problem of Phase Transition.

If time is sufficient, we will also talk about Er-godic Optimization or equivalently, the questionof ground states at temperature zero.

7.5. Travelling waves in a model for tumor invasionwith the acid-mediation hypothesis

Robert Marangell (The University of Sydney)


Dr Robert Marangell

In this talk, I will discuss how Geometric Singu-lar Perturbation Theory (GSPT) can be used toshow the existence of travelling wave solutions ina Gatenby-Gawlinski model. In particular, I willshow how GSPT can be used to show the exis-tence of a slow travelling wave with an interstitialgap. Such a gap has been observed experimen-tally, and we provide a mathematical frameworkfor its existence in terms of a dynamic transcriticalbifurcation.

7.6. Stable nonphysical waves in a model of tumourinvasion

Timothy Robertss (The University of Sydney)


Mr Timothy Roberts

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Travelling wave solutions to partial differentialequations appear in myriad applications, from biol-ogy to ecology and physics. However, establishingthe stability of such waves can be difficult. Moti-vated by the dynamical systems theory for ordinarydifferential equations (ODEs), a natural first stepin this process is to determine the spectral stabilityof the solution via the spectrum of the linearisedoperator. In this talk we apply this process toa biological model for cancer invasion driven byhaptotaxis developed by Perumpanani et al (1999)and further studied by Harley et al (2014) whichadmits a family of travelling shock solutions. Thisfamily of solutions can be naturally divided intofour classes of waves, based on the underlying ge-ometry of the corresponding steady state solutionsin phase space; three of these classes are physicallyreasonable, while the last is not. In doing so wereach a surprising conclusion: there exists a familyof nonphysical travelling wave solutions which arespectrally stable.

7.7. Characterising Chimeras by ConstructingNetworks

Michael Small (The University of Western Australia)


Prof Michael Small

We describe a new multi-channel time series analy-sis technique which represents a dynamical systemas a network (G). Each scalar variable from a mul-tichannel time series is encoded as an ordinal word,these words are then concatenated to provide aunique label for a node of G. Nodes are linked ifcorresponding words occur in temporal succession.The structural complexity of this graph can beshown to characterise the degree of synchrony orcoherence of the individual time series channels.In the case of dynamical behaviour on system oflow-dimensional systems connected via a connec-tivity or coupling network (which we denote C todistinguish it from G), each node can be thoughtof as emitting a scalar time series which we useto construct words and the concatenation of thesewords across all nodes of C creates a unique labelfor a node of G. As chimeras emerge and grow, thestructural complexity of G is shown to decrease.Using this construction we are then able to askhow C and G are related.

With Debora Correa and David M. Walker (Depart-ment of Mathematics and Statistics, University ofWestern Australia).

7.8. Dispersive quantisation

Dave Smith (Yale-NUS College)


Dave Smith, Natalie Sheils, Peter Olver, Beatrice

Pelloni

We consider the linear Schrodinger equation withhomogeneous linear boundary conditions. Weprove that in the case of pseudoperiodic bound-ary conditions the solution of the initial-boundaryvalue problem at specific times is a linear combi-nation of a certain number of copies of the initialdatum while at other times the solution appearsto be fractal. Further, we present the solution forgeneral homogenous linear boundary conditions interms of eigenvalues which can be found numeri-cally.

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8.1. Equilibrium states on Higher-rank Toeplitznoncommutative solenoids

Zahra Afsar (The University of Sydney)

09:00 Fri 7 December 2018 – Eng Sth 111

Dr Zahra Afsar

We consider a family of higher-dimensional non-commutative tori, which are twisted analoguesof the algebras of continuous functions on ordi-nary tori, and their Toeplitz extensions. Just assolenoids are inverse limits of tori, our Toeplitznoncommutative solenoids are direct limits of theToeplitz extensions of noncommutative tori. Weconsider natural dynamics on these Toeplitz al-gebras, and compute the equilibrium states forthese dynamics. We find a large simplex of equilib-rium states at each positive inverse temperature,parametrised by the probability measures on an(ordinary) solenoid. This is a joint work withAstrid an Huef, Iain Raeburn and Aidan Sims.

8.2. Isomorphisms of AC(σ) spaces for lineargraphs

Shaymaa Shawkat Kadhim Al-shakarchis

(University of New South Wales)

15:30 Wed 5 December 2018 – Eng Sth 111

Mrs Shaymaa Shawkat Kadhim Al-shakarchi

A theorem of Gelfand and Kolmogorov in 1939asserts that, the compact spaces X and Y arehomeomorphic if and only if the algebras of con-tinuous functions C(X) and C(Y) are isomorphicas algebras. In 2005, the algebras of absolutelycontinuous functions AC(σ) was defined by Doustand Ashton on a compact subset σ of the complexplane, and they studied whether there was a simi-lar link for these algebras between the propertiesof the domain σ and the Banach algebra propertiesof the function space. In one direction Doust andLeinert (2015) showed that if AC(σ1) is algebraisomorphic to AC(σ2) then σ1 and σ2 must behomeomorphic, so the interest now is in examiningthe converse implication.

In general the answer is no. We have examplesof infinite families of homeomorphic spaces {σn}for which the corresponding AC(σn) spaces aremutually nonisomorphic.

On the other hand, if one only considers sets σlying in restricted families, then one can obtainpositive results. Doust and Leinert showed that ifthe sets σ1 and σ2 are polygonal compact subsetsof the plane then AC(σ1) is algebra isomorphic toAC(σ2). It is conjectured that this result also holdsif σ1 and σ2 are finite unions of closed line segments.Examination of this case leads to an interesting

question in geometric graph theory which I willdiscuss.

8.3. Some results on Roman 2-domination in graphs

Faezeh Alizadehs (Shahid Rajaee Teacher Training

University)


Faezeh Alizadeh, Hamid Reza Maimani, Leila Parsaei

Majd, Mina Rajabi Parsa

For a graph G = (V,E) of order n, a Roman{2}-dominating function f : V → {0, 1, 2} has theproperty that for every vertex v ∈ V with f(v) = 0,either v is adjacent to a vertex assigned 2 underf , or v is adjacent to least two vertices assigned1 under f . In this paper, we classify all graphswith Roman {2}-domination number belonging tothe set {2, 3, 4, n− 2, n− 1, n}. Furthermore, weobtain some results about Roman {2}-dominationnumber of some graph operations.

8.4. A twisted tale of topological k-graphC*-algebras

Becky Armstrongs (The University of Sydney)

16:00 Tue 4 December 2018 – Eng Sth 111

Becky Armstrong

Directed graph C∗-algebras are a popular toolfor investigating various classes of C∗-algebras,and have provided a fruitful source of examples.These C∗-algebras have been generalised in manyways, including to k-graph C∗-algebras, topolog-ical graph C∗-algebras, and, more generally, totopological k-graph C∗-algebras; and to twistedk-graph C∗-algebras, which involve cohomologi-cal data in their construction. Recently, NathanBrownlowe and I initiated the study of twistedtopological k-graph C∗-algebras using C∗-algebrasassociated to product systems. For my PhDproject I have been examining an approach us-ing twisted groupoid C∗-algebras. In this talk,I will discuss twisted C∗-algebras associated totopological k-graphs, and I will present some exam-ples. (This is joint work with my PhD supervisors,Nathan Brownlowe and Aidan Sims.)

8.5. An application of recursive algorithm forinversion of linear operator pencils

Elizabeth Bradfords (University of South Australia)


Ms Elizabeth Bradford

There are numerous examples of systems that canbe represented by linear equations. In many casesthe system coefficient is an operator that dependson an unknown parameter. We are interested inwhat happens to the solution when we change this

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parameter. If the coefficient is a linear operatorpencil which depends on a single complex param-eter and the resolvent is analytic on a deletedneighbourhood of the origin, the resolvent can becalculated by different procedures. We calculatethe resolvent matrix using different recursive pro-cedures. In this talk I will show how these methodsare used to solve a pseudo-real problem consistingof an infinite set of differential equations.

8.6. Computations in Higher Twisted K-theory

David Leonard Brooks (The University of Adelaide)


Mr David Leonard Brook

Higher twisted K-theory is a highly contempo-rary area of research developed by Ulrich Pennigand Marius Dadarlat in 2016 as a generalisationof the topological K-theory and twisted K-theoryof the 20th century. Its construction involves re-placing the compact operators used in twistedK-theory with a special class of algebra known as“strongly self-absorbing C*-algebras”, which wereintroduced by Toms and Winter in 2005. In thistalk, I will summarise key definitions and resultsof topological and operator algebraic K-theory inorder to present a concise introduction to twistedand higher twisted K-theory, and explain why thisnewly defined construction is expected to yieldmeaningful results. In particular, I will presenta computation of the higher twisted K-theory ofodd-dimensional spheres and outline the directionof my future research.

8.7. Unitary representations of the Thompsongroup constructed with a category/functor methoddue to Jones

Arnaud Brothier (UNSW Sydney)


Dr Arnaud Brothier

The Thompson group is the group of homeomor-phisms of [0, 1] that are piecewise linear with slopesa power of 2 and breakpoints a dyadic rational. Itis one of the most studied discrete group whichstill remains very mysterious. Motivating in con-structing conformal field theories Jones recentlydiscovered a very general process that producesa unitary representation of the Thompson groupfrom very few data such as an isometry betweenHilbert spaces or a planar algebra together with acertain element. We will present this constructionand provide concrete examples. This is a jointwork with Jones.

8.8. Can we reconstruct a directed graph from itsToeplitz algebra?

Nathan Brownlowe (The University of Sydney)


Dr Nathan Brownlowe

Can we reconstruct a directed graph from itsToeplitz algebra? Do we need more data thanjust its Toeplitz algebra? In this talk I will answerthese questions. This is joint work with MarceloLaca, Dave Robertson, and Aidan Sims.

8.9. Maximum Generalised Roundness of RandomGraphs

Raveen Daminda de Silvas (University of New

South Wales)


Mr Raveen Daminda de Silva

Given a metric space, we can define its maximumgeneralised roundness, a non-negative real numberwhich determines properties including embeddingsinto Lp spaces. We investigate the distribution ofthe maximum generalised roundness of large ran-dom graphs, endowed with the path length metric,presenting experimental data and discussing thelimiting behaviour.

8.10. Asymptotic negative type properties of finiteultrametric spaces

Ian Doust (University of New South Wales)


Ian Doust, Stephen Sanchez and Anthony Weston

Negative type inequalities arise in the study ofembedding properties of metric spaces. For ex-ample a famous result of Schoenberg states thata finite metric space (X, d) may be isometricallyembedded in a Hilbert space if and only if it is of2-negative type, that is if

n∑i,j=1

d(zi, zj)2ηiηj ≤ 0

whenever z1, . . . , zn ∈ X and η1 + · · ·+ ηn = 0.

Unfortunately, even for small metric spaces nega-tive type inequalities often reduce to intractablecombinatorial problems. For some specific classesof finite metric space however, the last decade hasseen progress on obtaining sharper, more quanti-tative versions of these inequalities involving theso-called p-negative type gap. (This is roughly ameasure of how negative the left-hand side aboveneeds to be.)

Ultrametric spaces arise in many different areasof mathematics. Finite ultrametric spaces have p-negative type for all p. In this talk we shall discussthe very special properties of the p-negative typegap for these spaces.

8.11. Inequalities in Hermitian unital Banach∗-algebras

Silvestru Sever Dragomir (Victoria University)


Prof Silvestru Sever Dragomir

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In this presentation we introduce the quadraticweighted geometric mean for invertible elementsx, y in a Hermitian unital Banach ∗-algebra andreal number n. We show that it can be representedin terms of the usual geometric mean and providevarious inequalities for this mean under variousassumptions for the elements involved. For relatedwork on inequalities in Hermitian unital Banach ∗-algebras, see https://rgmia.org/v19.php, Articles:161-162, 165, 171-175 and 177-178.

8.12. Modular invariants for proper actions

Fei Han (National University of Singapore)


Assoc Prof Fei Han

Witten genus and elliptic genera are modular topo-logical invariants for manifolds, which are closelyrelated to representation of loop groups and thehypothetical index theory on free loop space aswell as the elliptic cohomology theory in algebraictopology. They find applications in problems ofpositive curvature and continuous group action onmanifolds. In this talk, we will briefly introducethese invariants and present our joint work withVarghese Mathai on generalizing them to openmanifolds with proper actions of open groups.

8.13. Pontryagin duality in higher Aharonov-Bohmeffect

Johnny Lims (The University of Adelaide)


Mr Johnny Lim

Pontryagin duality in cohomology depicts the closerelation between the ordinary integral homologyand its character group the circle-valued cohomol-ogy theory. In particular, there is a non-degeneratepairing map between them that provides a way for‘phase’ computation. One of the famous examplesbeing the Aharonov-Bohm effect in quantum me-chanics, which is the manifestation of Pontryaginduality in cohomology in degree 1. The extensionof this notion to a generalised cohomology the-ory, such as K-theory, then plays a role in higherAharonov-Bohm effect in Type II String theory.Moreover, an analytic Pontryagin duality pairingin K-theory can be formulated explicitly and infact it encodes much more data than that of incohomology. In this talk, I will explain this no-tion in more detail and discuss the Pontryaginduality pairing between even K-homology K0 andcircle-valued K0 theory.

8.14. The Chern character of differential gradedalgebras and an Index Theorem

Matthias Ludewig (The University of Adelaide)


Dr Matthias Ludewig

We define a Fredholm module over a differentialgraded algebra A to be parity preserving linearmap c : A → L(H) for some graded Z2-gradedHilbert space H, together with an odd self-adjointoperator Q on L(H) satisfying certain algebraicand analytic conditions. In particular, for appli-cations, it is too strong to require c to be a rep-resentation, and also [Q, c(a)] = c(da) need notalways hold. However, it turns out that one canstill construct a cocyle Ch(Q, c) of such a Fredholmmodule, which is a generalization of the famouscocycle of Jaffe, Lesniewski and Osterwalder to thegraded case; we call this the Bismut-Getzler Cherncharacter, since in case A is given by the differen-tial forms on an even dimensional spin manifold,with c the Clifford multiplication and Q the Diracoperator, this cocycle turns out to be related to aloop space path integral considered by Bismut andGetzler. In the case of an ungraded algebra, thepairing of the JLO-cocycle with Connes’ Cherncharacter of a projection in A turns out to be givenby an index; this is the non-commutative index the-orem by Getzler and Szenes. We show that in ourgraded situation, there is a similar theorem, whichinvolves the pairing our cocycle with the Bismut-Chern character of a projection, the latter beingconstructed in a special case by Getzler, Jonesand Petrack, who were motivated by Bismut’sloop space considerations. Our results completean essential part of the Getzler-Jones-Petrack pro-gramme of infinite dimensional localization in theloop space. This is joint work with Batu Gneysu.

8.15. Equilibrium in operator algebraic dynamicalsystems

Michael Arthur Mampustis (University of

Wollongong)

09:00 Thu 6 December 2018 – Eng Sth 111

Mr Michael Arthur Mampusti

In this talk, an operator algebraic dynamical sys-tem is a C*-algebra with an action of a locallycompact group. When the locally compact groupis the real line, we consider the action as a timeevolution of the C*-algebra, and an equilibriumstate as a state which is invariant under the action.We consider Kubo-Martin-Schwinger (KMS) statesfor operator algebraic dynamical systems, whichare, in particular, equilibrium states.

In 2008, Ionescu and Watatani associated a Cuntz-Pimsner algebra to a Mauldin-Williams graph.The Cuntz-Pimsner algebra is a C*-algebra whichcomes with a canonical action of the circle. Liftingthis action to the real line, we obtain a operatoralgebraic dynamical system. We discuss the KMSstates of this operator algebraic dynamical system,and the information that these states recover aboutthe Mauldin-Williams graph.

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8.16. C*-algebras associated to graphs of groups

Jessica Murphys (The University of Sydney)


Ms Jessica Murphy

Graph of groups arise naturally as the quotientobjects of groups acting on trees, and play a fun-damental role in Bass-Serre theory. A C∗-algebratheory for graphs of groups has recently been intro-duced, and as part of their analysis, it is shown thatthere is a natural C∗-subalgebra isomorphic to adirected graph C∗-algebra built from paths in thegraph of groups. In this talk I will discuss the rela-tionship between graph of groups C∗-algebras andthese C∗-subalgebras corresponding to directedgraphs. (This is a joint work with my supervisor,Nathan Brownlowe)

8.17. A Noncommutative Generalisation of aProblem of Steinhaus

Thomas Scheckters (University of New South Wales)


Mr Thomas Scheckter

Responding to work of Revesz on a problem ofSteinhaus, Komlos showed that every integrablesequence of random variables contains a subse-quence which “satisfies the strong law of largenumbers”, such that the sequence of Cesaro aver-ages converges almost everywhere. We solve anopen problem of Randrianantoanina by extendingthis result to arbitrary semifinite von Neumannalgebras. In this talk we discuss the history ofthe problem, what it means to study almost every-where convergence in the noncommutative setting,the technical obstructions of the noncommutativesetting, and several related results.

8.18. A Dixmier-Douady Theory for Fell Algebrasand their associated Brauer Group

Nicholas Seatons (University of Wollongong)


Mr Nicholas Seaton

In 1963, J. Dixmier and A. Douady classified con-tinuous trace C∗-algebras with spectrum T up toMorita equivalence by classes in the 2nd Cech co-homology group. They also associated a Brauergroup to the spectrum of these C∗-algebras. In2011, A. An Huef, A. Kumjian and A. Sims gener-alised this to classify Fell algebras, however theydid not construct a Brauer group. In this talk,we will discuss their Dixmier-Douady theory anddescribe an approach to find the Brauer group forFell algebras over their spectrum.

8.19. Crystallographic T-duality and superBaum-Connes conjecture

Guo Chuan Thiang (The University of Adelaide)


Dr Guo Chuan Thiang

A relatively unexplored direction for the Baum–Connes conjecture is for super-groups. The sim-plest example is glide reflection, generating theinteger group but with the even-odd grading: thegraded K-theory of the group algebra is isomorphicto the twisted K-homology of the classifying space,and both already have 2-torsion. This is one exam-ple in a whole zoo of crystallographic T-dualities,discovered recently with my collaborator K. Gomi,which had been anticipated from string theory andthe physics of topological matter.

8.20. The magnetic spectral gap-labellingconjecture and some recent progess

Mathai Varghese (The University of Adelaide)


Prof Mathai Varghese

Given a constant magnetic field on Euclidean spaceRp determined by a skew-symmetric (p×p) matrixΘ, and a Zp-invariant probability measure µ onthe disorder set Σ which is by hypothesis a Cantorset, where the action is assumed to be minimal,the corresponding Integrated Density of States ofany self-adjoint operator affiliated to the twistedcrossed product algebra C(Σ) oσ Zp, where σ isthe multiplier on Zp associated to Θ, takes on val-ues on spectral gaps in the magnetic gap-labellinggroup. The magnetic frequency group is definedas an explicit countable subgroup of R involvingPfaffians of Θ and its sub-matrices. We conjec-ture that the magnetic gap labelling group is asubgroup of the magnetic frequency group. Wegive evidence for the validity of our conjecture in2D, 3D, the Jordan block diagonal case and theperiodic case in all dimensions, as well as for allprincipal solenoidal tori.

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9.1. The long-time behaviour of the pluriclosed flowon Lie groups

Romina Melisa Arroyo (University of Queensland)


Dr Romina Melisa Arroyo

The pluriclosed flow is a geometric flow that evolvespluriclosed Hermitian structures (i.e. Hermitianstructures for which its 2-fundamental form satis-fies ∂∂ω = 0) in a given complex manifold. Theaim of this talk is to discuss the asymptotic be-haviour of the pluriclosed flow in the case of left-invariant structures on Lie groups. More precisely,invariant structures on 2-step nilmanifolds and al-most abelian solvmanifolds. We will analyze theflow and explain how a suitable normalization con-verges to pluriclosed solitons, which are self-similarsolutions to the flow. Moreover, we will show thatsome of those limits are shrinking solitons, which isan unexpected feature in the solvable case. We willalso exhibit the first example of a homogeneousmanifold on which a geometric flow has some so-lutions with finite extinction time and some thatexist for all positive times.

This is a joint work with Ramiro Lafuente (TheUniversity of Queensland).

9.2. On the Existence of Stable Unduloids ofDimension Eight

David Hartley (University of Wollongong)


Dr David Hartley

The stability of constant mean curvature hyper-surfaces is an important topic in mathematics andinfluences problems such as the dynamics of the vol-ume preserving mean curvature flow. We considerthe case where the hypersurfaces have free bound-ary contained in parallel planes, this results in theperiodic Delaunay hypersurfaces. They includespheres (which are always stable), cylinders (whichare stable at large radii), and nodoids (which areunstable). The final case of unduloids is morecomplex. All unduloids of dimension two throughseven are unstable, but there exists stable undu-loids of dimension nine and greater. In this talk,we will consider the missing case of whether thereexists stable unduloids of dimension eight. We willalso work towards finding a criterion to determineif a specific unduloid is stable or unstable.

9.3. Higgs bundles and foliations

Pedram Hekmati (The University of Auckland)


Dr Pedram Hekmati

The existence of Hermitian-Einstein metrics onholomorphic bundles is intimately tied to the no-tion of stability. In this talk I will explain howthis correspondence works in the setting of holo-morphic bundles on foliated manifolds and if timeallows, its extension to transverse Higgs bundles.

9.4. Some sharp Levy-Gromov type isoperimetricinequalities

Kwok-Kun Kwong (The University of Sydney)


Dr Kwok-Kun Kwong

The Levy-Gromov isoperimetric inequality statesthat under a positive Ricci curvature lower bound,the area-to-volume ratio of a domain is not smallerthan that of a certain ball in the comparison space.In this talk, I will present my recent work on a newsharp Levy-Gromov type isoperimetric inequalitywhich involves the cut distance. There are tworemarkable features of the result. One is that weallow the Ricci curvature lower bound to be arbi-trary. The second one, which is more surprising,is that we obtain a lower bound for the volumeinstead of an upper bound (of course the boundcannot depend only on the boundary area, but alsoon its cut distance). This is in contrast with theclassical isoperimetric inequality, the Levy-Gromovisoperimetric inequality and the Bishop-Gromovvolume comparison theorem, all of which providean upper bound of the volume of a domain either interms of its boundary area, or in terms of the vol-ume of its counterpart in the comparison space. Iftime allows, I will also discuss another isoperimet-ric inequality which involves the extrinsic radiusof a domain.

9.5. Hermitian curvature flow on complex Liegroups

Ramiro Augusto Lafuente (The University of

Queensland)


Dr Ramiro Augusto Lafuente

In this talk we will report on recent progresson the study of the Hermitian curvature flow ofleft-invariant metrics on complex unimodular Liegroups. After reducing the evolution to the Ricciflow-type equation ∂tgt = −Ric1,1(gt), we showthat the solution gt always exist for all positivetimes, and that the renormalization (1 + t)−1gtconverges in Cheeger-Gromov sense as t → ∞to a non-flat, left-invariant, self-similar solution(soliton). This is joint work with M. Pujia and L.Vezzoni.

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9.6. Closed ideal planar curves

James McCoy (The University of Newcastle)


Assoc Prof James McCoy

We use a gradient flow to deform closed planarcurves to curves with least variation of geodesiccurvature in the L2 sense. Given a smooth initialcurve we show that the solution to the flow existsfor all time and converges smoothly to a multiply-covered circle, provided the length of the evolvingcurve remains bounded under the flow. Curvesin any homotopy class with initially small lengthcubed times the energy do enjoy a uniform lengthbound under the flow. This is joint work with BenAndrews, Glen Wheeler and Valentina Wheeler.

9.7. Regularity of the dbar equation in degeneratingfamilies

Brett Parker (Monash University)


Dr Brett Parker

Pseudo-holomorphic curves satisfy a nonlinearPDE called the dbar equation. As the dbar oper-ator is elliptic, standard regularity results applyto the dbar equation from a fixed domain, or asmooth family of domains. I will explain whathappens in a degenerating family of domains. Thisresult is important for analysing the moduli spaceof pseudo-holomorphic curves because curves inthis moduli space can degenerate, forming nodesand bubbles.

9.8. Some integral estimates for Ricci flow in fourdimensions

Miles Simon (Magdeburg University)


Prof Miles Simon

We present some integral estimates which hold forany solution to Ricci flow on a closed four dimen-sional manifold. Under the extra assumption thatthe scalar curvature is bounded, we show that atany potential finite singular time, the manifoldcan at most degenerate to a C0 Riemannian orb-ifold. We show that the flow can then be continuedthrough this singularity, using the orbifold Ricciflow.

9.9. Reduced SU(2) Seiberg-Witten Equationscompared to SU(2) Ginzburg-Landau equations

Ahnaf Tajwar Tahabubs (The University of

Adelaide)


Mr Ahnaf Tajwar Tahabub

To sidestep the computational difficulty of theYang-Mills invariants for 4-manifolds, NathanSeiberg and Edward Witten developed two abeliannon-linear partial differential equations (called

Seiberg-Witten Equations) that essentially pro-vide the same information but under mild assump-tions. However, the abelian nature of the U(1)twisted spin group used for these SW equationsmake them far easier to study. Remarkably, Wit-ten showed that the dimension reduction (to twodimensions) gives precisely the Ginzburg-Landauequations for super-conductors. This relationshipcombined with that determined by Taubes withPseudo-holomorphic curves provides better insightinto the theory of super-conductors. In this talk Ishall briefly construct the non-abelian SW equa-tions for an orientable compact 4-manifold andspecialise to the case for SU(2) twisted spin group.This will lead into the dimensional reduction ofthese equations and an outline of how these equa-tions compare to the non-abelian SU(2) Ginzburg-Landau theory in analogy to Witten’s result.

9.10. Volume preserving flow and geometricinequalities in hyperbolic space

Yong Wei (Australian National University)


Dr Yong Wei

In this talk I will describe some recent work (jointwith Ben Andrews (ANU) and Xuzhong Chen (Hu-nan)) on the application of volume preserving flowfor hypersurfaces to prove geometric inequalitiesin hyperbolic space. I will first discuss some earlierresults which give relations between quermassin-tegrals for horospherically convex hypersurfaces.Then I will discuss two generalisations: First, weextend these inequalities under the weaker condi-tion of positive intrinsic curvature; and second, weprove some sharper family of inequalities whichhold for horospherically convex hypersurfaces.

9.11. Length-constrained curve diffusion

Yuhan Wus (University of Wollongong)


Ms Yuhan Wu

We show that initial closed curves suitably closeto a circle flow under the length-constrained curveto round circles in infinite time. We provide anestimate on the total length of time for which suchcurves are not strictly convex. We further showthat there are no closed translating solutions to theflow and that the only closed rotators are circles.

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10.1. Knot tabulation: a software odyssey

Benjamin Burton (University of Queensland)


Benjamin Burton

The tabulation of all prime knots up to a certainnumber of crossings was one of the founding prob-lems of knot theory in the 1800s, and continues tobe of interest today. Here we take a tour throughthe many and varied software challenges requiredto tabulate all 350 million prime knots up to 19crossings. Sights along the way include combinato-rial, algebraic and geometric computations, alongwith a mix of theoretical algorithm design andpractical algorithm engineering.

10.2. Twisted K-theory of compact Lie groups andextended Verlinde algebras

Chi-Kwong Fok (The University of Adelaide)


Dr Chi-Kwong Fok

In a series of recent papers, Freed, Hopkins andTeleman put forth a deep result which identifies thetwisted K-theory of a compact Lie group G withthe representation theory of its loop group LG.Under suitable conditions, both objects can beenhanced to the Verlinde algebra, which appearsin mathematical physics as the Frobenius algebraof a certain topological quantum field theory, andin algebraic geometry as the algebra encoding in-formation of moduli spaces of G-bundles over Rie-mann surfaces. Verlinde algebras for G with niceconnectedness properties have been well-known.However, explicit descriptions of such for discon-nected G are lacking. In this talk, I will explainthe various aspects of the Freed-Hopkins-TelemanTheorem and present partial results on an exten-sion of the Verlinde algebra with disconnected G,with a view towards its relation to a generalisationof moduli spaces called twisted moduli spaces. Thetalk is based on work in progress joint with DavidBaraglia and Varghese Mathai.

10.3. Particles of the first generation

David G Glynn (Flinders University)


Dr David G Glynn

Journey starts benignly with “Theorems of pointsand planes in three-dimensional projective space”(2010), tunnels through “A rabbit hole betweengeometry and topology” (2013), and roller-coastsinto physics “Cosmology = Topology/Geometry:mathematical evidence for the holographic princi-ple” (2016). Buzzing particles swarm over a calmsea of quarks. Everything in triplicate.

10.4. Cobordism map on PFH induced byelementary Lefschetz fibration

Chen Guanheng (The University of Adelaide)


Dr Chen Guanheng

Periodic Floer homology (PFH) is a three dimen-sion analogy of Taubes’ Gromov invariant for map-ping torus. Y-J. Lee and C.H.Taubes show that itis equivalent to Seiberg Witten cohomology. Onenaturally expects that this equivalence extendsto TQFT level. Motivated by this conjecture, weshow that the cobordism map on PFH induced byelementary Lefschetz fibration is well defined, inaddition, we give an explicit computation for it.

10.5. Virtual and welded tangles via operads

Iva Halacheva (The University of Melbourne)


Ms Iva Halacheva

Usual tangles in 3-space were described by Jonesusing planar algebras, which one can think of asalgebras over the operad of planar tangles. Bar-Natan and Dancso introduced the concept of cir-cuit algebras, for which the planarity condition isdropped, to describe virtual tangles, i.e. tanglesin thickened surfaces. We relate circuit algebrasto modular operads, introduced by Getzler andKapranov and used to study surface gluing in topol-ogy, with interesting implications for both sides.

10.6. Triangulations of Solid Tori and Dehn Fillings

Sophie Hams (Monash University)


Ms Sophie Ham

It remains an open conjecture that every knot com-plement has a geometric triangulation. This con-jecture has been proved for a class of knots knownas 2-bridge knots. However, it is not known formany additional classes of knots. In this talk, wepresent the main ideas for a proof of this conjecturefor a large class of knots called highly twisted knots.The method involves first using the explicit geom-etry of fully augmented links from which highlytwisted knots are constructed to determine trian-gulations of the initial manifolds, then applyingresults by Gue’ritaud and Schleimer on changesin triangulations under Dehn filling to fully aug-mented links [Gue’ritaud and Schleimer, Geom.Topol, 2010]. This should prove that highly twistedknots have a geometric triangulation. Gue’ritaudand Schleimer found canonical triangulations ofDehn fillings of links that satisfied certain generic-ity assumptions. However, these assumptions donot hold for many examples arising in practice.

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We generalise their results to extend to broaderclasses of links, including many examples of fullyaugmented links.

10.7. Counting Non-Crossing Partitions on Surfaces

Jian He (Monash University)


Dr Jian He

Given a surface with boundary and a number ofpoints on its boundary components, a non-crossingpartition is a way to join those points up into sev-eral non-intersecting polygons. The special case,where only bigons are allowed, corresponds tothe enumeration of arc diagram on the surface.The count of arc diagram is known, and it hasa rich structure. In particular it has polynomialbehaviour in the number of points on each bound-ary component, and the leading coefficients of thepolynomial are the intersection numbers on themoduli space of curves of the topological type ofthe given surface. We will show that the generalcount of non-crossing partitions follows a similartopological recursion and exhibits all the interest-ing behaviours of the arc diagram count.

This is joint work with Norman Do and DanielMathews.

10.8. Trisections and their complexity

Boris Lishak (The University of Sydney)


Dr Boris Lishak

A trisection is a way to represent a smooth 4-manifold as a gluing of three 1-handlebodies -an analogue of Heegaard splittings in dimension4. The intersection of the handlebodies is a 2-dimensional closed surface. We will discuss howthe genera of the surface and of the handlebodiesdepends on the fundamental group of the manifold.

10.9. Supersymmetric path integrals: Integratingdifferential forms on the loop space

Matthias Ludewig (The University of Adelaide)


Dr Matthias Ludewig

We construct an integral map for differential formson the loop space of Riemannian spin manifolds.For example, Bismut-Chern character forms areintegrable with respect to this map, with their in-tegrals given by indices of Dirac operators. More-over, the map satisfies a localization principle,which provides a rigorous background for pathintegral proofs of the Atiyah-Singer Index theoremby Alvarez-Gaum, Atiyah, Witten, Bismut andothers. This is joint work with Florian Hanisch.

10.10. Perpendicularity in Ancient Babylon

Daniel Francis Mansfield (University of New South

Wales)


Dr Daniel Francis Mansfield

This talk is about the origins of perpendicular-ity and an ancient form of proto-trigonometryfrom Mesopotamia which is almost 4000 years old.The talk is based on my 2017 article on Plimpton322 and an upcoming article about another longlost tablet which shows how this ancient proto-trigonometry was used.

10.11. Tropical geometry, the topological vertex,and Gromov-Witten invariants of Calabi-Yau 3-folds,

Brett Parker (Monash University)


Dr Brett Parker

Complex manifolds with normal crossing divisors,and normal crossing degenerations, have a naturallarge scale with a tropical, or piecewise integral-affine structure. Moreover, on this large scale,holomorphic curves correspond to piecewise-lineartropical curves. I will draw some pictures, andexplain some beautiful aspects of this tropical cor-respondence in the Calabi-Yao 3-fold setting, re-lated to the Strominger–Yau–Zaslow approach tomirror symmetry: In this case, the large scale is a3-dimensional integral affine manifold with singu-larities along a 1-dimensional graph. The verticesof this singular graph come in two types: positiveand negative, and the relative Gromov–Witten in-variants around the positive vertices contain thetopological vertex of Aganagic, Klemm, Marinoand Vafa.

10.12. Tiling the Euclidean and Hyperbolic planeswith ribbons

Vanessa Robins (Australian National University)


Dr Vanessa Robins

Patterns built from repeating motifs appear inall cultures and have long been studied in art,mathematics, engineering and science. Most math-ematical work has focussed on patterns in theEuclidean plane (the book “Tilings and Patterns”by Grunbaum and Shephard contains a compre-hensive survey of the field up to the mid 1980s)but the importance of hyperbolic geometry as amodel for natural forms is increasingly recognised.An example that inspires this work is the discov-ery that co-polymer molecules consisting of threemutually immiscible arms can self-assemble intostructures modelled by stripes on the gyroid triplyperiodic minimal surface. The gyroid surface hasgenus three in its smallest side-preserving transla-tional unit cell, and therefore has the hyperbolic

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plane as its simply-connected covering space. Its3d space-group symmetries induce a non-euclideancrystallographic group generated by hyperbolicisometries that are known explicitly. Stripe pat-terns on the gyroid lift via the covering map totilings of the hyperbolic plane by infinitely longstrips, or ribbons.

The defining property of a ribbon tile is the exis-tence of a translation isometry that maps a giventile back onto itself as well as preserving the tilingpattern of the whole space. I will describe howto classify and enumerate crystallographic ribbontilings of the hyperbolic plane by viewing them asdecorations of 2-orbifolds.

10.13. Compactification of the Space of ConvexProjective Structures on Surfaces

Dominic Tates (The University of Sydney)


Mr Dominic Tate

In 1984 Morgan and Shalen describe a means ofcompactifying the Teichmuller space of hyperbolicstructures on surfaces which realises a boundarypoint of the Teichmuller space by an action on anR-tree. It is known that in the setting of higherTeichmuller theory, where the group of hyperbolicisometries, PSL(2,R) is replaced by PSL(n,R), theaction described by Morgan and Shalen on R-treesis generalised to an action on Euclidean buildingsof rank n-1. In the case of PSL(3,R), Parreau(2015) provided a geometric description of actionswhich represent some of the points on the bound-ary of the higher Teichmuller space, which possessthe additional quality that the length spectrum ofthe PSL(3, R) action on a rank 2 building continu-ously extends the length spectrum of the holonomygroups of convex projective structures on the in-terior of the space of convex projective structures.I generalise Parreau’s construction to all rationalpoints on the boundary of the higher Teichmullerspace.

10.14. Commensurability classification of certainright-angled Coxeter groups

Anne Thomas (The University of Sydney)


Pallavi Dani, Emily Stark and Anne Thomas

Two abstract groups are commensurable if theyhave isomorphic finite index subgroups. We givethe commensurability classification for certain fam-ilies of right-angled Coxeter groups. A key stepis proving that these Coxeter groups are virtuallyfundamental groups of geometric amalgams of sur-faces. We then use covering-theoretic argumentsand Euler characteristic to establish our classifica-tion.

10.15. Oriented geodesics in the three-sphere

Adam Woods (The University of Melbourne)


Mr Adam Wood

In 1989 Werner Fenchel gave a classification oforiented lines and their common perpendiculars inhyperbolic space with an application to the con-struction and description of right angled hexagons.In this talk we discuss these notions in the sphericalsetting.

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11.1. Sharp weighted estimates for square functionsassociated to operators on homogeneous spaces

Anh Bui (Macquarie University)


Dr Anh Bui

Let X be a metric spaces with a doubling measureand let L be a linear operator in L2(X) whose heatkernels satisfy the Gaussian upper bound. Thispaper proves sharp Lpw norm inequalities for squarefunctions associated to L including the verticalsquare functions, the Lusin area integral squarefunctions and the Littlewood-Paley g-functions.It is worth noticing that we do not assume anyregularity condition on the heat kernel.

11.2. Scattering of the nonlinear Klein-Gordonequations

Xing Cheng (Monash University)


Dr Xing Cheng

In this talk, we will show the scattering of themass-critical nonlinear Klein-Gordon equations.To prove the scattering, we rely on the bilinearrestriction estimate to give the profile decompo-sition. We also need to use the solution of themass-critical nonlinear Schrodinger equation to ap-proximate the nonlinear profile in the large scalecase. Then we can prove the scattering by usingthe concentration-compactness/rigidity method.

11.3. Optimisation in the Construction ofSymmetric and Cardinal Wavelets on the Line

Neil Kristofer Dizons (The University of Newcastle)


Neil Dizon, Jeffrey Hogan, Joseph Lakey

Ingrid Daubechies’ construction of compactly sup-ported smooth orthogonal wavelets on the line hav-ing multiresolution structure, coupled with otherdesirable properties, relied heavily on techniquesof complex analysis, many of which are unavail-able in the higher-dimensional setting. Alterna-tively, Franklin, Hogan, and Tam developed tech-niques which have been successful in producingDaubechies’ wavelets, among others, from uniformsamples of the so-called quadrature filters associ-ated with the multiresolution structure. In thistalk, we present an alternative construction of com-pactly supported smooth orthogonal wavelets byconsidering samples of the scaling functions andassociated wavelets as variables. This allows forthe construction of scaling functions and waveletswith optimal cardinality and symmetry properties.

11.4. Maximal operators with generalised Gaussianbounds on non-doubling Riemannian manifolds withlow dimension

Hong Chuong Doans (Macquarie University)


Mr Hong Chuong Doan

Let L be a non-negative self-adjoint operatoron L2(R1]R2). In this talk, we will investi-gate the boundedness of the maximal operatorassociated with the heat semi-group M∆f(x) :=supt>0 |e−t∆f(x)| where ∆ is the Laplace-Beltramioperator acting on the non-doubling manifold withtwo ends R1]R2. By using the subordinationformula, we obtain the weak type (1, 1) and Lp

(1 < p ≤ ∞) boundedness of the maximal operator

Tkf(x) := supz∈S0µ|(z√L)ke−z

√Lf(x)| where k is

a non-negative integer and

S0µ := {z ∈ C : | arg z| < µ} with 0 < µ <

π

4.

11.5. BMO spaces associated to operators onnon-doubling manifolds with ends

Xuan Duong (Macquarie University)


Prof Xuan Duong

Consider a non-doubling manifold with ends M =Rn]Rm where Rn = Rn × Sm−n for m > n ≥ 3.We say that an operator L has a generalised Pois-

son kernel if√L generates a semigroup e−t

√L

whose kernel pt(x, y) has an upper bound similar

to the kernel of e−t√

∆ where ∆ is the Laplace-Beltrami operator on M . An example for op-erators with generalised Gaussian bounds is theSchrodinger operator L = ∆ + V where V is anarbitrary non-negative locally integrable potential.Our aim is to introduce the BMO space associatedto an operator with generalised Poisson boundswhich serves as an appropriate setting for certainsingular integrals with rough kernels to be boundedfrom L∞(M) into this new BMO space. We canalso show that the John-Nirenberg inequality holdsand we give an interpolation theorem for a holo-morphic family of operators which interpolatesbetween Lq(M) and the new BMO space. As anapplication, we show that the holomorphic func-tional calculus m(

√L) is bounded from L∞(M)

into the new BMO, and bounded on Lp(M) for1 < p <∞.

11.6. Bergman and Bergman-Toeplitz operators onpseudoconvex domains

Tran Vu Khanh (University of Wollongong)


Dr Tran Vu Khanh

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In this talk, we discuss about regularity propertiesof Bergman and Bergman-Toeplitz operators onsome classes of pseudoconvex domains in Cn.

11.7. An inversion technique for linear operatorpencils in Hilbert space

Geetika Verma (University of South Australia)


Dr Geetika Verma

We explain an inversion technique to find the gen-eralised resolvent of a linear operator pencil inHilbert space that is singular at the origin. Weoutline a recursive procedure that reduces the orig-inal resolvent problem to a sequence of equivalentresolvent problems on smaller spaces by using anincreasing sequence of orthogonal projections toprogressively extract the singular terms in theLaurent series expansion of the resolvent. The ex-traction terminates after a finite number of stepsif the reduced resolvent becomes nonsingular atthe origin in which case the original resolvent hasa finite order pole at the origin. If the processcontinues ad infinitum we appeal to Zorn’s lemmato justify the existence of an upper bound on thesequence of orthogonal projections. Thus we de-termine the singular component of the Laurentseries and show that the original resolvent has anisolated essential singularity at the origin. We il-lustrate our remarks by considering the inversionof a linear operator pencil defined by taking theLaplace transform of an infinite system of ordinarydifferential equations.

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12.1. A generalized Temperley-Lieb algebra in thechiral Potts model

Remy Alexander Addertons (The Australian

National University)


Mr Remy Alexander Adderton

The Temperley-Lieb algebra (TLA) plays a centralrole in the integrability of some key models instatistical mechanics. In this talk I will describea new TLA generalization for the N-state chiralPotts model given by N-1 coupled Temperley-Liebalgebras. This is analogous to the well knownrelation between the quantum Potts chain andthe Temperley-Lieb algebra. I will also discusssome representations of the coupled Temperley-Lieb algebra in the one- and two-boundary cases.

12.2. Some exact Lyapunov exponents for randommatrix products

Peter Forrester (The University of Melbourne)


Prof Peter Forrester

It was nominated by Kingman that “Pride of placeamong the unsolved problems of subadditive er-godic theory must go to the calculation of theLyapunov exponent”. In this talk I’ll survey someknown results where the Lyapunov exponent – andsometimes spectrum – for random matrix productscan be calculated exactly, and I’ll present somenew examples too.

12.3. Hidden solutions of discrete systems

Nalini Joshi (The University of Sydney)


Prof Nalini Joshi

Hidden solutions are well known in irregular singu-lar limits of differential equations. These solutionsare not able to be identified uniquely through con-ventional analysis, because free parameters identi-fying the solution lie hidden beyond all orders of adivergent asymptotic expansion. In previous stud-ies, we identified such solutions of discrete Painleveequations, known as q-PI, d-PI, and d-PII, in thelimits where their independent variable goes toinfinity. In this talk, we extend the investigationto further solutions and to new types of equations.

Through such analysis, we determine regions of thecomplex plane in which the asymptotic behaviouris described by a power series expression, and findthat the behaviour of these asymptotic solutionsshares a number of features with the tronquee andtri-tronquee solutions of corresponding differentialPainleve equation.

12.4. A new framework and extensions oflog-aesthetic curves in industrial design by integrablegeometry

Kenji Kajiwara (Kyushu University)


Kenji Kajiwara, Jun-ichi Inoguchi, Kenjiro T. Miura

and Wolfgang Schief

In this talk we discuss a new framework of the log-aesthetic curves (LAC) in industrial design basedon the similarity geometry, where LAC is under-stood as a similarity geometric analogue of theEuler’s elasticae. We discuss two basic characteri-zations of LAC: (i) the rigid motion of integrabledeformation of plane curves (ii) variational princi-ple. Then we discuss some new outcomes based onthis formulation, namely (i) integrable discretiza-tion of LAC (ii) space curve extension of LAC.

12.5. Finding rational integrals of rational discretemaps

Reinout Quispel (La Trobe University)


Prof Reinout Quispel

We present a novel method for finding rational firstand second integrals of rational maps/ordinarydifference equations.

12.6. Ground-state energies of the open and closedp+ ip-pairing models from the Bethe Ansatz

Yibing Shens (The University of Queensland)


Yibing Shen, Phillip S. Isaac, Jon Links

We first study the p+ ip Hamiltonian isolated fromits environment (closed model) through the BetheAnsatz solution and consider the case of a largeparticle number. A continuum limit approximationis applied to compute the ground-state energy. Wediscuss the evolution of the solution curve, andthe limitations of this approach. We then consideran alternative approach that transforms the BetheAnsatz equations to an equivalent form in termsof the real-valued conserved operator eigenvalues.This approach also generalizes to accommodateinteraction with the environment (open model).

12.7. Certain subgroups of the Coxeter groups andsymmetry of discrete integrable equations

Yang Shi (Flinders University)


Ms Yang Shi

We explore some unique properties of the Coxetergroups in the context of discrete integrable systems.In particular, we look at the applications of the

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Normalizer theory of parabolic subgroups in thestudies of discrete Painleve equations.

12.8. Helical solitons in vector modifiedKorteweg–de Vries equations

Yury Stepanyants (University of Southern

Queensland)


Prof Yury Stepanyants

We study existence and structure of helical solitonsin the vector modified Korteweg–de Vries (mKdV)equations, one of which is completely integrableby Inverse Scattering Method, whereas anotherone is nonintegrable. The latter one describesnonlinear waves in various physical systems, in-cluding plasma and chains of particles connectedby elastic springs. By using the dynamical systemmethods such as the blow-up near singular pointsand the construction of invariant manifolds, weconstruct helical solitons by the efficient shootingmethod. The helical solitons arise as the resultof co-dimension one bifurcation and exist along acurve in the velocity-frequency parameter plane.Examples of helical solitons are constructed nu-merically for the non-integrable equation and com-pared with exact solutions in the integrable vectormKdV equation. The stability of helical solitonswith respect to small perturbations is confirmed bydirect numerical simulations. Examples of interac-tions of helical solitons with each other and withplane solitons will be presented for both integrableand non-integrable equations

12.9. Schubert calculus and quantum integrablesystems

Paul Zinn-Justin (The University of Melbourne)


Assoc Prof Paul Zinn-Justin

We shall discuss the recent breakthrough in solvingthe 19th century problem of Schubert calculususing quantum integrability. This is joint workwith A. Knutson.

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13.1. Multiscale modelling of fibre-reinforcedhydrogels for tissue engineering

Mike Chen (The University of Adelaide)


Dr Mike Chen

Tissue engineering aims to grow artificial tissuesin vitro to replace those in the body that havebeen damaged through age, trauma or disease.A recent approach to engineer artificial cartilageinvolves seeding cells within a scaffold consisting ofan interconnected three dimensional printed latticeof polymer fibres combined with a cast or printedhydrogel, and subjecting the construct (cell-seededscaffold) to an applied load in a bioreactor. Akey question is to understand how the appliedload is distributed throughout the construct to themechanosensitive cells.

To address this, we employ homogenisation the-ory to derive macroscale governing equations forthe effective material properties of the compos-ite, where we treat the fibres as a linear elasticmaterial and the hydrogel as a poroelastic mate-rial and exploit the disparate length scales (smallinter-fibre spacing compared with construct dimen-sions). This description reflects the orthotropicnature of the composite. To validate the model,solutions from finite element simulations of themacroscale, homogenised equations are comparedto experimental data describing the unconfinedcompression of fibre-reinforced hydrogels.

13.2. Modelling Non-Uniform Growth in CylindricalYeast Colonies

Anthony John Gallos (The University of Adelaide)


Mr Anthony John Gallo

Laboratory experiments have shown that yeast cangrow vertically upwards from an agar plate to forma cylindrical colony. However, the nature in whichnutrients diffuse through the colony and how thisaffects cell proliferation within the colony is notfully understood. In general, the nutrient distri-bution will be non-constant and hence there willbe spatially dependent cell proliferation. In thistalk, we present an agent-based discrete model tosimulate non-uniform growth using a probabilitydistribution to model the non-constant nutrientgradient and biased cell proliferation. Analytic ex-pressions are derived to approximate the (average)trajectories of the initial cells in the colony, andthis provides a way to analyse the non-uniformgrowth within the colony.

13.3. Pattern Avoidance in Genomics

Yoong Kuan Gohs (University of Technology,

Sydney)


Mr Yoong Kuan Goh

One part of genomics research is gene rearrange-ments. There is a tantalising connection betweenthis field and the field of pattern avoidance withincombinatorics. In this talk, I will describe the con-nection between these two fields and the possibilityin applying some outcomes of pattern avoidanceresearch to solve the problems in gene rearrange-ments.

13.4. Learning advantages in evolutionary games

Maria Kleshninas (The University of Queensland)


Miss Maria Kleshnina

The idea of incompetence as a learning or adap-tation function was introduced in the context ofevolutionary games as a fixed parameter. However,live organisms usually perform different nonlinearadaptation functions such as a power law or ex-ponential fitness growth. Here, we examine howthe functional form of the learning process mayaffect the social competition between different be-havioral types. Further, we extend our results forthe evolutionary games where fluctuations in theenvironment affect the behavioral adaptation ofcompeting species and demonstrate importanceof the starting level of incompetence for survival.Hence, we define a new concept of learning advan-tages that becomes crucial when environments areconstantly changing and requiring rapid adapta-tion from species. This may lead to the evolution-arily weak phase when even evolutionary stablepopulations become vulnerable to invasions.

13.5. Who cares? Or, when does paternal care arisein primates?

Danya Rose (The University of Sydney)


Dr Danya Rose

Paternal care is a rare trait among primates, withmales of most species preferring a competitiveapproach to gaining paternities and spending lit-tle time interacting with or protecting their ownyoung. Males who care for their young risk forego-ing opportunities to compete with other males forextra paternities. Affecting the costs and rewardsof either strategy are biological issues such as lac-tational amenorrhea, pregnancy duration, and lifehistory, which we include in a new model of the

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interplay between care and competition. We ex-plore this model in an effort to characterise someconditions under which paternal care might arise.

13.6. Predicating saturation in models of genomerearrangement in polynomial time

Jeremy Sumner (University of Tasmania)


Dr Jeremy Sumner

Genome rearrangement models provide an evolu-tionary comparison of genomes with identifiablysimilar content, such as genes or other large scalegenomic units. These models focus on differencesin structure, such as the order that these unitsappear in the genome, and describe molecular evo-lution via rearrangements. For certain domains oflife, such as bacteria, where evolution is compli-cated and often dominated by “horizontal” trans-mission of genetic material (via lateral gene trans-fer events), this somewhat coarse-grained approachis eminently sensible.

However, genome rearrangements are mathemati-cally combinatorial in nature and the calculationof evolutionary distance with respect to a gen-eral rearrangement model is inherently of factorialcomplexity. Various heuristics have been used toaddress this issue; however many of these demandquite stringent, unrealistic conditions on the al-lowed rearrangements.

We are exploring an approach which applies repre-sentation theory to calculate evolutionary distancebetween circular genomes as a maximum likelihoodestimate (MLE) of time elapsed. This approachopens the door to numeric approaches where ap-proximate solutions and/or partial results may beobtained in polynomial time. In particular, somepairs of genomes do not have an MLE distance asthe relative arrangement of their genomes is at sto-chastic saturation with respect to the model underconsideration. We are able to predict this situationusing a (quadratic time) eigenvalue evaluation.

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14.1. ‘Learning to Communicate’ and‘Communicating to Learn’

Amie Albrecht (University of South Australia)

09:30 Thu 6 December 2018 – HL 422

Dr Amie Albrecht

Mathematics is a language of its own, and studentsneed to learn to communicate effectively throughboth the written and spoken word. Conversely,communication is also an important part of learn-ing mathematics. By articulating and justifyingtheir mathematical ideas, and listening to andmaking sense of the ideas of others, students de-velop and refine their conceptual understanding.Yet few tertiary mathematics courses provide stu-dents with explicit opportunities, encouragementand support in developing effective communicationskills.

In this talk I will discuss assessment and classroomstrategies designed to elicit exploratory thinking,encourage revision, and support growth in oralpresentation and mathematical writing skills. Thisapproach has been developed over five years in‘Developing Mathematical Thinking’, a course de-signed for pre-service maths teachers at the Uni-versity of South Australia.

The major assessment item in this course requiresstudents to communicate the results of an in-depthinvestigation of a self-selected topic via a writtenreport and an oral presentation. I will describe astructure that supports each student in choosinga topic, writing a draft report, providing peercritique, revising work in response to feedback,and preparing a high-quality final report.

Student competence and confidence with oral com-munication is progressively developed throughweekly mini-talks which gradually increase inlength, and audience familiarity and size. Eachweek focuses on different skills such as deliv-ery, body language, organisation, and visual aids.Guided peer feedback and self-reflection help stu-dents continually improve.

Focusing on both ‘learning to communicate’ and‘communicating to learn’ by having students talkabout their evolving mathematical ideas whilealso learning to communicate mathematically hasturned out to be a powerful strategy to propeltheir mathematical development.

14.2. First year engineering mathematics diagnostictesting

Roland Dodd (Central Queensland University)

16:00 Tue 4 December 2018 – HL 422

Dr Roland Dodd, Antony Dekkers

The mathematics capability of students, enteringthe Central Queensland University (CQU) engi-neering program, has a very large variation. Manyengineering mathematics students commence theirundergraduate studies with significant mathemat-ics deficiencies in their fundamental mathematicsskills.

Every year at CQU an engineering mathematicsskills analysis is offered to incoming first year stu-dents, consistently revealing problems in founda-tion mathematics concepts and principles. Thispaper discusses a comparison and analysis of theseengineering mathematics diagnostic test resultssince introduction in 2016. Outcomes for furtheruse and integration in the CQU engineering pro-gram are presented.

14.3. Educating On-line Software

Diane Donovan (The University of Queensland)

16:00 Fri 7 December 2018 – HL 422

Prof Diane Donovan

In this talk I will reflect on the principles of a“good” learning environment for mathematics andthe challenge of using technology to enhance thisprocess.

The primary aim of this talk will be to promotediscussion on how to personalize technology drivenlearning environments. So how we can foster real-time interactions both between the students andwith the demonstrator. Are we providing plat-forms which allow for individuality in learning butalso in thinking? Can we efficiently provide di-rect communication between students experiencedacademics?

I will propose and discuss some approaches whichI have trialed in recent years.

14.4. You can teach old dogs new tricks if youknow them well

William Guo (Central Queensland University)

16:30 Tue 4 December 2018 – HL 422

Prof William Guo

After finishing the final examination of an ad-vanced mathematics unit at Central QueenslandUniversity (CQU), a distance student in her mid-30s wrote to me “... I know it can be a littlebit difficult to teach this old dog new tricks, butwith perseverance I think I just might have learnta couple of things.” She is among the one-thirdof students who are 35 years or up in a typicalunit at CQU, one of many regional universities inAustralia. By the definition of ‘adult learner’ or‘mature student’ as a person who is 25 years or upand is involved in forms of learning, the percentage

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of mature students would be close to 50 percentin many mathematics units at CQU. These ma-ture students, particularly those 35 years or up,are typically returning adults who pursue highereducation with more life experience, work commit-ments and/or family responsibilities at CQU.

As reported in literature, mature students tend tobe self-initiated, self-directed, self-determined, andself-planned. The traditional pedagogical methodsbased on the premise of transmission of knowledgeand skills from the teacher to the adolescent stu-dents may not meet the needs of mature students.My experience in teaching mature students, par-ticularly those 35 years or up enrolled in my intro-ductory, intermediate, and advanced mathematicsclasses since 2013 at CQU, shares above common-alities possessed by mature students. However,my experience also indicates that any alternativeoverall delivery approach tailored to incorporatesuch commonalities is insufficient to guide mostmature students going through these mathematicsunits with confidence. An approach of ‘a baselinefor all’ plus ‘an adaptive addition to individual’has been much more appropriate to the maturestudents, particularly those 35 years or up enrolledin my mathematics classes. This talk will presentsome cases of teaching mathematics units for ma-ture students from 35 to over 80 years using thisapproach in the past a few years at CQU.

14.5. Student learning and feedback in highereducation mathematics

David Hartley (University of Wollongong)

14:00 Tue 4 December 2018 – HL 422

Dr David Hartley

In this talk I will give a brief review of literatureon feedback, highlighting its importance in thestudent learning process. There is a lack of theorythat is specific to higher education mathematicsand I discuss why the more general theories maynot be as relevant to this context. I will thengo through some reflections on how I have seenstudents use feedback during my last 21 monthsas a learning developer providing student support.

14.6. Reflections on a kaleidoscope of multi-faceted,cross-disciplinary mathematics support. Feeding thegrowing appetite

Deborah Jackson (La Trobe University)

16:30 Fri 7 December 2018 – HL 422

Dr Deborah Jackson

Quality mathematics support is now an essentialingredient of student success in many and varieddisciplines. Such support needs to capture the in-terest and enthusiasm of the students and answerthe requests for sound mathematics support by

lecturers and coordinators, in a wide range of sub-jects or disciplines. To be successful, mathemat-ics support should also be enriching, interesting,colourful, relevant and interactive, as well as flexi-ble and multi-faceted. It should not only answerspecific questions, but encourage deep learning,and give students confidence in translating disci-pline problems into mathematical ones, and viceversa. Catering for multi-campus and online re-mote learning adds more dimensions and dilemmasthat need to be addressed. We discuss the multi-faceted mathematics support provided by La TrobeUniversity’s Maths Skills Program and Maths Hub,which have encapsulated a whole range of supportto multi-disciplines to appease a growing appetite.

14.7. Benefits and challenges of peer-assessmentfor online subjects

Simon James (Deakin University)

10:00 Thu 6 December 2018 – HL 422

Dr Simon James

The use of peer-assessment has the potential to pro-vide students with an engaging experience, allow-ing them to become aware of multiple approachesto meeting assignment requirements, and to thinkcritically on assignment objectives. For some tasks,peer assessment could also help alleviate workloadissues for academics and provide students withvaluable feedback. This presentation reflects onthe experiences of implementing peer-assessmentfor a mathematical coding project in a unit de-signed for pre-service teachers.

14.8. Mathematics and Indigenous Culture

Carolyn Kennett (Macquarie University)

14:30 Tue 4 December 2018 – HL 422

Carolyn Kennett, Madeleine Dawson, Ruby Foster

In this talk, I will talk about the National In-digenous Science Education Program and presentsome work done by two students working with meon a mathematics outreach project as part of theprogram.

14.9. Choose-your-own assessment

Heather Lonsdale (Curtin University)

09:00 Thu 6 December 2018 – HL 422

Dr Heather Lonsdale

Assessing a diverse range of learning outcomes, fora diverse range of learners, is always a challenge.In mathematics students are often used to a moretraditional form of test-based assessment, but thisdoes not always allow them to demonstrate theirfull range of capabilities.

I will talk about some of my work on alternativeassessment options, but in particular about thechoices that students have been able to make asto how they undertake these. For oral assessment

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of problem-solving, which can seem daunting tostudents unaccustomed to it, students were giventhe choice of the frequency and the format of theseassessments — including whether to be assessedas a group or individually. For a mathematicalmodelling unit, students were given the option ofcompleting an application-based modelling projectin place of test-based assessment. For a range ofunits, the final exam was set as optional if studentswere able to demonstrate the learning outcomes inother ways during the semester.

In this practice-based talk, I will present theseexperiences and my reflections, and hope to promptdiscussion about the ways we assess and the choiceswe give students in demonstrating their learning.

14.10. Comparing the Quality of LearningOutcomes

Chi Mak (University of New South Wales)

15:00 Fri 7 December 2018 – HL 422

Dr Chi Mak

The School of Mathematics and Statistics of theUniversity of New South Wales (UNSW) has usedonline formative assessments as supplements totutorials in various first year Mathematics coursessince 2008. From 2015, the pattern of face-to-facetutorial progressively changed and reduced fromtwo per week to one. The other tutorial has beenreplaced by an online tutorial which composes ofvideos, other materials and online formative assess-ments. The purpose of the formative assessmentsis to provide problems with guidance for studentsto apply what they learnt from the videos etc. Im-mediate feedback is provided to facilitate learning.

In general, surveys show that students are satis-fied with the new tutorial and online assessmentarrangements. To evaluate the change of qual-ity of learning Mathematics, Freislich and Bowen-James conducted a specific research into one of thecourses. A few questions were identified from thewritten final exam in the year 2015 (prior to thechange) and similar questions in the year 2016 (af-ter the change). The questions were marked againusing a new marking scheme based on the SOLOtaxonomy [Biggs and Collis, Evaluating the qual-ity of learning: The SOLO taxonomy, New York:Academic Press]. They marked a random sampleof scripts and have some interesting findings.

In another course, the assessment pattern waschanged so that 50% of the final assessment markis contributed from the online assessment on theskills to be mastered in this course. The Math-ematics writing skills is assessed through a writ-ten assignment and the final written exam. It isintended that a similar method of Freislich andBowen-James noted above will be used to comparethe quality of learning outcomes between the oldand new assessment patterns.

14.11. Making mathematics teachers: Beliefs aboutmathematics and mathematics teaching and learningheld by academics who teach future teachers

Margaret Marshman (University of the Sunshine

Coast)

15:30 Tue 4 December 2018 – HL 422

Dr Margaret Marshman, Prof Merrilyn Goos

(University of Limerick)

Secondary mathematics pre-service teachers area significant cohort of students within universitymathematics classes. Often these students expe-rience mathematics teaching and learning differ-ently across their initial teacher education. I willpresent the results of a survey of Australian math-ematicians and mathematics educators who teachsecondary mathematics pre-service teachers, docu-menting their beliefs about mathematics, its teach-ing, and its learning. The findings are presentedusing descriptive statistics, t-tests and analysis ofinterview data with a small subset. In general,participants had a Problem-solving view of mathe-matics and those with a background in educationtended to have more agreement with a Problem-solving approach to teaching.

14.12. Authoring accessible ‘Tagged PDF’documents using LATEX

Ross Moore (Macquarie University)

14:30 Fri 7 December 2018 – HL 422

Dr Ross Moore

Several ISO standards have emerged for whatshould be contained in PDF documents, to sup-port applications such as ‘archivability’ (PDF/A)and ‘accessibility’ (PDF/UA). These involve theconcept of ‘tagging’, both of content and struc-ture, so that smart reader/browser-like softwarecan adjust the view presented to a human reader,perhaps afflicted with some physical disability. Inthis talk we will look at a range of documentswhich are fully conformant with these modernstandards, mostly containing at least some mathe-matical content, created directly in LATEX. The ex-amples are available on the author’s website: http://web.science.mq.edu.au/~ross/TaggedPDF/.

The desirability of producing documents this waywill discussed, along with aspects of how muchextra work is required of the author. Also on theabove website is a ‘five-year plan’ proposal howto modify the production of LATEX-based scien-tific publications to adopt such methods. Thiswill involve cooperation between academic pub-lishers and a TUG working group. The proposalPDF is itself produced to be fully accessible, com-plying with both PDF/UA-1 and PDF/A-2a stan-dards; get it at http://web.science.mq.edu.au/

~ross/TaggedPDF/PDF-standards-v2.pdf.

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http://web.science.mq.edu.au/~ross/TaggedPDF/

http://web.science.mq.edu.au/~ross/TaggedPDF/

http://web.science.mq.edu.au/~ross/TaggedPDF/PDF-standards-v2.pdf

http://web.science.mq.edu.au/~ross/TaggedPDF/PDF-standards-v2.pdf


14.13. Conceptual Considerations in the Transitionto University Mathematics: The Case for Limits as aThreshold Concept

Greg Oates (University of Tasmania)

13:30 Fri 7 December 2018 – HL 422

Dr Greg Oates; Dr Robyn Reaburn (UTAS); Dr

Kumudini Dharmasada (UTAS); Dr Michael Brideson

(UTAS)

Threshold concepts remain relatively unexploredin mathematics, despite suggestions that the trou-blesome nature of such concepts pose a criticalbarrier to student understanding of mathematics.Many studies have identified student difficultieswith limits, and their findings point to a strong like-lihood that limits do indeed constitute a thresholdconcept in mathematics. This paper describes theinitial results in a study that sought to investigatestudents’ understanding of limits and differentia-tion from the prospective of Threshold Concepts.While the findings to date do not provide conclu-sive evidence for limits as a threshold concept, theydo reinforce the troublesome nature of the limitconcept, and suggest some important implicationsfor the teaching of limits consistent with previousstudies. In particular, the findings suggest we needto be more explicit in the attention we pay to po-tential changes in the language and the way weconceptualise limits and asymptotes as studentstransition from school to university.

14.14. Transition between school and university —placement test and bridging course

Jelena Schmalz (University of New England)

14:00 Fri 7 December 2018 – HL 422

Dr Jelena Schmalz

UNE introduced a new structure for first-yearMaths units in 2016. The Bridging Course andthe Placement Test were developed and introducedas a part of this new structure. The purpose ofthe placement test is to help students determinewhich Mathematics units they should enrol. Thismaximises students’ chances of success and sat-isfaction throughout their degree. The BridgingCourse is a free course open to anyone enrolled atUNE that aims to help build up knowledge andfill gaps in mathematical skills to prepare studentsfor studying first year mathematics units at UNE,and is also helpful to any students in schools ordisciplines which require quantitative skills. ThisBridging Course allows to start any time, andwork at ones own pace. In the talk we introducethe Placements test and the Bridging Course, anddiscuss the impact of these innovations.

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15.1. Knotting probabilities for polygons in latticetubes

Nicholas Beaton (The University of Melbourne)

16:00 Wed 5 December 2018 – Eng Nth 132

Dr Nicholas Beaton

Self-avoiding polygons are the standard statisticalmechanical model for ring polymers in dilute solu-tion. In three dimensions polygons can be knotted,and it is a celebrated result of Sumners and Whit-tington that sufficiently long polygons are knottedwith high probability. However, self-avoiding poly-gons in 3D are not solvable, and in this context“sufficiently long” is very long — perhaps on theorder of 105.

I will discuss a variant of this model, namely poly-gons restricted to semi-infinite tubes of the cubiclattice. This is a simple model of ring polymers innanochannels, and is solvable, being characterisedby a finite transfer matrix. It is thus possible to ex-actly compute growth rates and critical exponents,and (when the matrix is not too big) develop astatic Monte Carlo method that allows the sam-pling of polygons directly from a chosen Boltzmanndistribution. In this way knotting probabilities canbe accurately estimated.

This is joint work with Chris Soteros and JeremyEng.

15.2. The conditionally integrable diffusionequation with nonlinear diffusivity 1/u

Philip Broadbridge (La Trobe University)

15:30 Tue 4 December 2018 – Eng Nth 132

Prof Philip Broadbridge

The nonlinear diffusion equation in one time andtwo space dimensions,

∂u

∂t= ∇ ·

[1

u∇u],

is known to have an infinite dimensional Lie pointsymmetry group, including a free pair of conju-gate harmonic functions. Each choice of complexanalytic function f(z) will lead to a symmetry re-duction to a non-integrable PDE in one time andone space dimension. There is some advantage infinding a direct mapping from a chosen functionf(z) to an infinite dimensional class of explicit so-lutions of the nonlinear diffusion equation. Thatclass is given here. The solutions satisfy constant-flux boundary conditions on any contour. Theincreasing solutions have initial condition u = 0and the decreasing positive solutions are extin-guished in finite time. With diffusivity D = 1/u,the solutions apply to diffusion of an electron gas.With D = 1/(c − u), they apply to fluid flow inporous media.

15.3. Constructions of 1 + 1-dimensionallattice-gauge theories and the Thompson group

Arnaud Brothier (UNSW Sydney)


Dr Arnaud Brothier

I will present work in progress joint with AlexanderStottmeister. Bringing together ideas developedby Vaughan Jones between subfactor theory andconformal field theory, and from lattice-gauge the-ory, we construct 1 + 1-dimensional multi-scalemodels that are connected to representations ofthe Thompson group or its rotation subgroup. Theconstruction is operator-algebraic and works forany compact group with a certain family of mea-sures on its unitary dual. Formally we consider anet of C*-algebras equipped with states indexedby binary trees. The limit gives us a von Neumannalgebra together with a state. When the groupis abelian we can give a very precise descriptionof this limit. I will present this construction withtwo main examples based on the group U(1) andits associated family of Gibbs states coming fromthe Kogut-Susskind Hamiltonian.

15.4. One-point recursions of Harer-Zagier type

Anupam Chaudhuris (Monash University)


Mr Anupam Chaudhuri

Harer and Zagier computed the virtual Euler char-acteristics of moduli spaces of smooth curves viathe enumeration of ribbon graphs with one face.They found a recursion for this enumeration, whichwe refer to as a one-point recursion. In this talk,we explore other enumerative problems that satisfyanalogous one-point recursions with the aim of un-covering a common theme between these problems.In particular, we will show that monotone Hurwitznumbers satisfy a one-point recursion.

15.5. Capillary-Gravity Surface over a Bump:Critical Surface Tension

Jeongwhan Choi (Korea University)


Jeongwhan Choi, S.I. Whang, J.S. Kim, S.H. Yun

We concern forced surface waves on an incompress-ible, inviscid fluid in a two dimensional channelwith a small bump on a horizontal rigid flat bottomand nonzero surface tension on the free surface. Ithas been known that a nondimensional wave speed,called Foude number, is near 1 and a nondimen-sional surface tension, called Bond number, is near1/3, the KdV theory fails and a time dependentfifth order KdV equation, called Kawahara equa-tion, can be derived to model the wave motion on

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the free surface. In this study, a time dependentKawahara equation with a forcing is studied boththeoretically and numerically. Existence theoremand various numerical results are presented.

15.6. A limit theorem for the coupling time of thestochastic Ising model

Timothy Garoni (Monash University)


Assoc Prof Timothy Garoni

The coupling time of the stochastic Ising model isthe random time required for processes started inthe all-plus and all-minus states to coalesce, whencoupled in the natural way. We show that, forany natural d, and sufficiently high temperature,the (appropriately standardised) coupling time ofthe stochastic Ising model on d-dimensional toritends weakly to a Gumbel distribution. This isjoint work with Tim Hyndman, Zongzheng Zhouand Andrea Collevecchio.

15.7. Self-avoiding walks with restricted end-points

Iwan Jensen (Flinders University)


Dr Iwan Jensen

Any SAW has a minimal bounding rectangle, whichis the unique rectangle such that the SAW does notextend beyond the rectangle and the SAW touchesall the borders of the rectangle. We study SAWswith prescribed end-points within the minimalbounding rectangle. Among these models are thewell-known ordinary unrestricted SAW, SAWs withone or both end-points attached to a surface, andSAWs confined to a wedge. Spanning walks arisenaturally in the study of so-called bridges whileyet another model is related to the problem ofSAWs crossing a square. We determine the criticalexponents γ from series analysis and for the newmodels we conjecture the exact value.

15.8. Determinantal polynomials, vortices andrandom matrices: an exercise in experimentalmathematical physics

Anthony Mays (The University of Melbourne)


Dr Anthony Mays

Inspired by the interpretation of eigenvalues ofrandom matrices as a gas of interacting particleswe develop a toy model of vortex or particle dy-namics using determinantal polynomials of randommatrices. By introducing quaternionic structureswe generate vortex/anti-vortex systems, and fromstudying the phase surface of the associated wave-function, we identify topological rules governingthe creation and annihilation of the vortices. Wealso discuss an interpretation of annihilation eventsin terms of quaternionic states. This exploratory

project is very much in the vein of experimentalmathematics, and so contains many avenues forfurther investigation.

15.9. Two-point functions of random walk modelson high-dimensional boxes

Zongzheng Zhou (Monash University)


Dr Zongzheng Zhou

The self-avoiding walk (SAW) on Zd is known todisplay the same large-scale behaviour as simplerandom walk (SRW) when d is large. In particular,the SAW and SRW Green’s functions are knownto display the same asymptotics when d ≥ 5. Onfinite boxes, however, where SAWs must have fi-nite length, this SAW-SRW correspondence breaksdown. To recover such a correspondence, we in-troduce a random-length random walk (RLRW),and rigorously derive its Green’s function. Bycombining these general RLRW results with theasymptotic walk-length distribution of the SAWon the complete graph, we obtain an explicit con-jecture for the SAW Green’s function on high-dimensional tori, both at criticality and withina broad family of scaling windows. Using a ran-dom walk representation of the Ising model, dueto Aizenman, these conjectures extend naturallyto the Ising model, where they then shed light on anumber of questions under current debate by com-putational/theoretical physicists. Finally, we willalso discuss the case of free boundary conditions,where the RLRW model again clarifies a numberof actively debated questions.

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16. Number Theory

16.1. On the growth of product of partial quotients

Ayreena Bakhtawars (La Trobe University)

15:30 Wed 5 December 2018 – IW B17

Miss Ayreena Bakhtawar

The metrical theory of continued fractions is oneof the major subjects in the study of continuedfractions. From Dirichlet’s (1842) and Legender’s(1808) results we conclude that to find a goodrational approximation to an irrational numberwe only need to focus on its convergents. Let[a1(x), a2(x), . . .] be the continued fraction expan-sion of a real number x ∈ [0, 1). In this talk, wefocus on the growth rate of an(x)an+1(x) whichis tightly connected with the Dirichlet improvablenumbers. More precisely, we determine the Haus-dorff dimension of the set

F (φ) = {x ∈ [0, 1) : an+1(x)an(x) ≥ φ(n) forinfinitely many n ∈ N andan+1(x) < φ(n) for allsufficiently large n ∈ N}

where φ : N→ R+ is an arbitrary positive function.This in return contribute to the metrical theoryof continued fractions This is a joint work withPhilip Bos.

16.2. Explicit bounds on exceptional zeroes ofDirichlet L-functions

Matteo Bordignons (University of New South Wales

Canberra)

16:00 Tue 4 December 2018 – IW B17

Mr Matteo Bordignon

We aim to improve the upper bound for the excep-tional zeroes of Dirichlet L-functions. This is doneimproving on explicit estimate for L′(σ, χ) for σclose to unity.

16.3. Hausdorff Measure and DirichletNon-Improvable Numbers

Philip Boss (La Trobe University)


Mr Philip Bos

Let Ψ : [1,∞)→ R+ be a non-decreasing function,an(x) the n’th partial quotient of x and qn(x) thedenominator of the n’th convergent. The set ofΨ-Dirichlet non-improvable numbers

G(Ψ) :={x ∈ [0, 1) : an(x)an+1(x) > Ψ

(qn(x)

)for infinitely many n ∈ N

},

is related with the classical set of 1/q2Ψ(q)-approximable numbers K(Ψ) in the sense thatK(3Ψ) ⊂ G(Ψ). Both of these sets enjoy thesame s-dimensional Hausdorff measure criterionfor s ∈ (0, 1). We prove that the set G(Ψ) \K(3Ψ)

is uncountable by proving that its Hausdorff di-mension is the same as that for the sets K(Ψ) andG(Ψ). This gives an affirmative answer to a ques-tion raised by Hussain-Kleinbock-Wadleigh-Wang(2017).

This is a joint work with Ayreena Bakhtawar andMumtaz Hussain.

In my talk, I will set the scene and sketch theproof.

16.4. Heights and isogenies of Drinfeld modules

Florian Breuer (The University of Newcastle)


Prof Florian Breuer

It is known that if two elliptic curves defined overa number field are linked by an isogeny of degreed, then the difference of their Faltings heights isbounded by 1

2 log d. A similar result also holds forthe Weil heights of their j-invariants.

In this talk, I will present analogous results forDrinfeld modules. In particular, one can associateseveral different heights to a Drinfeld module, andthe key lies in comparing these heights. This isjoint work with Fabien Pazuki.

16.5. Square-free numbers in short intervals

Michaela Cully-Hugills (University of New South

Wales Canberra)


Ms Michaela Cully-Hugill

The smallest theoretical interval length containingat least one square-free number was given by Fi-laseta and Trifonov in 1992, which applied for allsignificantly large numbers. The explicit versionof their proof will be presented, as well as the re-sulting explicit interval length that can be used forspecific ranges. An outline of the classical resultwill also be given, as well as how it can be used inconjunction with Filaseta and Trifonov’s result togive an explicit result for the range of all positiveintegers not covered by computation.

16.6. On the geometric Steinitz problem

Anand Rajendra Deopurkar (Australian National

University)

09:30 Fri 7 December 2018 – IW B17

Dr Anand Rajendra Deopurkar

Let L/K be a finite extension of number fields.Associated to this extension is the discriminantideal D in the ring of integers of K. The Steinitzinvariant is a refinement of the discriminant; it isa square root of D in the ideal class group. Anopen problem in number theory is to characteriseideal classes that can arise as Steinitz invariants. I

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16. Number Theory

will describe a complete solution to the geometricanalogue of this problem, obtained jointly withAnand Patel, using the geometry of vector bundleson algebraic curves.

16.7. Measure theoretic laws in Diophantineapproximation

Mumtaz Hussain (La Trobe University)

09:30 Thu 6 December 2018 – IW B17

Dr Mumtaz Hussain

In this talk, I will briefly discuss some new measuretheoretic methods and techniques which helps indetermining the size of limsup sets in Diophantineapproximation.

16.8. Overpartitions

Thomas Morrill (UNSW Canberra)


Dr Thomas Morrill

We give a brief introduction to these combina-toric objects and their connections to automorphicforms, and present upcoming work in overparitiongenerating series.

16.9. Carmichael polynomials over finite fields

Min Sha (Macquarie University)


Dr Min Sha

Motivated by Carmichael numbers, we introduceCarmichael polynomials over finite fields, estab-lish Korselt’s criterion for them, and estimate thenumber of such polynomials of fixed degree. (Thisis joint work with Sunghan Bae and Su Hu.)

16.10. The efficient computation of Splitting Fieldsusing Galois groups

Nicole Sutherland (The University of Sydney)


Dr Nicole Sutherland

We consider the efficient computation of splittingfields of polynomials over arithmetic fields usingthe Galois group algorithm of Fieker and Kluners.I will report on recent work for polynomials overglobal function fields and considerations which areunique to prime characteristic. One particularsplitting field allows a polynomial to be solved byradicals, an original motivator of Galois groups,and I will also describe the extra computationnecessary to gain a splitting field in this form andthe considerations here which are unique to primecharacteristic.

16.11. Zeroes of the zeta-function: mind the gap!

Timothy Trudgian (UNSW Canberra)


Dr Timothy Trudgian

Several open problems (with wine/cash prizes fortheir resolution) will be presented on gaps betweenzeroes of the Riemann zeta-function. I shall outlinethe history of the problem as well as some ongoingwork joint with Caroline Turnage-Butterbaugh atCarleton College, MN, USA.

16.12. On modular Nekrasov–Okounkov formulas

Ole Warnaar (The University of Queensland)


Prof Ole Warnaar

The Nekrasov–Okounkov formula is a far-reachinggeneralisation of Euler’s classical product formulafor the generating function of integer partitions. Inthis talk I will discuss several modular analogues ofthe Nekrasov–Okounkov formula based on Little-wood’s decomposition (a two-dimensional analogueof Euclidean division) and variations thereof. Iftime permits I will discuss connections with theHilbert scheme of points in the plane.

16.13. On multiplicative independence of rationalfunction iterates

Marley Youngs (University of New South Wales)


Mr Marley Young

We give lower bounds for the degree of multiplica-tive combinations of iterates of rational functions(with certain exceptions) over a general field, es-tablishing the multiplicative independence of saiditerates. This leads to a generalisation of Gao’smethod for constructing elements in the finite fieldFqn whose orders are larger than any polynomialin n when n becomes large.

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17. Optimisation

17.1. Game Theory and Machine Learning forComplex Networked Systems

Tansu Alpcan (The University of Melbourne)


Assoc Prof Tansu Alpcan

There is a growing need to manage the efficiencyand security of complex networked systems, whichare no longer operated by a single agent, but re-quire the coordination of many agents who man-age different parts of the network. Game the-ory provides an excellent analytical framework tomodel such multi-agent problems. However, mod-ern data and computation-intensive systems chal-lenge traditional game and system-theoretic formu-lations, which suffer from scalability issues whenthere are large numbers of agents and complex,non-convex system representations. An emerg-ing grand challenge is to better understand howsystem disciplines (communication/control/signalprocessing) and game theory will benefit from dataand algorithm-oriented methods of machine learn-ing. Similarly, machine learning methods need acounterpart of the formalism that underpin systemdisciplines and game theory. This talk will discussthese challenges within an optimisation contextand using specific examples.

17.2. Doubleton Projections in Hilbert Spaces

Theo Bendits (The University of Newcastle)


Mr Theo Bendit

We present a simple, non-constructive, sufficientcondition for a normed-closed subset C of a realHilbert Space to admit a point that projects ontoprecisely two points of C. We examine some conse-quences, limitations, and possible generalisationsof this result, making reference to its relevance tothe study of Chebyshev sets.

17.3. Generalized convexity

Thi Hoa Buis (Federation University Australia)


Ms Thi Hoa Bui

Some important generalised convexity propertieslike quasiconvexity, explicit quasiconvexity andpsedoconvexity are not stable when the function isperturbed by a linear functional with sufficientlysmall norm. In this talk, we will consider a classof generalised convex functions so-called robustlyquasiconvex function that some expected optimisa-tion properties remain stable under a small linearperturbation. We will recall some known results

for continuously differentiable functions, and dis-cuss on how to deal with non-smooth functionsusing the mean of Frchet subdifferentials.

Besides, some other important of generalized con-vexity properties are introduced for further discus-sion.

17.4. Adaptive Douglas-Rachford splittingalgorithm for the sum of two operators

Minh N. Dao (The University of Newcastle)


Dr Minh N. Dao

The Douglas-Rachford algorithm is a classical andpowerful splitting method for minimizing the sumof two convex functions and, more generally, find-ing a zero of the sum of two maximally monotoneoperators. Although this algorithm has been wellunderstood when the involved operators are mono-tone or strongly monotone, the convergence theoryfor weakly monotone settings is far from beingcomplete. In this work, we propose an adaptiveDouglas-Rachford splitting algorithm for the sumof two operators, one of which is strongly mono-tone while the other one is weakly monotone. Withappropriately chosen parameters, the algorithmconverges globally to a fixed point from which wederive a solution of the problem. When one opera-tor is Lipschitz continuous, we prove global linearconvergence which sharpens recent known results.

17.5. A fixed point operator in discrete optimisation

Andrew Craig Eberhard (Royal Melbourne Institute

of Technology)


Prof Andrew Eberhard

I will discuss some duality structures that haveappeared in discrete optimisation in conjunctionwith studies of discrete proximal point algorithm,augmented Lagrangian duality, some supportingtheory for the “Feasibility Pump” and more re-cently with regard to Stochastic Integer program-ming. A common theme appears involving a fixedpoint operator associated with the local minimaof a regularised dual function. This enables theone to describe some MIP heuristics in terms of arelated continuous optimisation problem, enablingthe use of ideas from continuous optimisation.

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17. Optimisation

17.6. The Interior Epigraph Directions Algorithmfor Nonsmooth and Nonconvex ConstrainedOptimization and applications

Wilhelm Freire (Universidade Federal de Juiz de

Fora)


Prof Wilhelm Freire

We present an algorithm that uses a generalizedLagrangian duality for solving nonsmooth and non-convex constrained optimization problems. Themethod considers the dual problem induced by ageneral augmented Lagrangian to generate a se-quence of points (dual variables) in the interior ofthe epigraph of the dual function. The method is amodification of the deflected subgradient method.In the inner iteration of the algorithm, we find aprimal minimizer of the Lagrangian, which in turnis used to update the dual variables in the outeriteration. We describe new strategies for minimiz-ing the Lagrangian and solve some academic andapplied problems.

17.7. On continuity/discontinuity of the optimalvalue of a long-run average optimal control problemdepending on a parameter

Vladimir Gaitsgory (Macquarie University)


Prof Vladimir Gaitsgory

We will discuss conditions, under which the opti-mal value of a long run average optimal controlproblem is continuous/discontinuous with respectto a perturbation parameter. A distinctive featureof our approach is that the perturbation analy-sis of the optimal control problem is carried outon the basis of the perturbation analysis of theinfinite-dimensional linear programming problemthat is equivalent to the former. The presentationwill be based on results obtained in collaborationwith V. S. Borkar, M. Mammadov and L. Manic

17.8. The two-train separation problem

Phil Howlett (University of South Australia)


Prof Phil Howlett

When a train travels from one station to the nexton level track the strategy that minimizes energyconsumption for a given journey time is maxi-mum acceleration, speedhold at the optimal driv-ing speed, coast and maximum brake. If two trainstravel along the same track in the same directionthen the usual safety constraint is that the trainsmust be separated by two signals at all times. Ifboth trains follow the optimal single train strategythen the safety constraint may be violated. Whatis the optimal strategy for each train when a safeseparation constraint is imposed?

17.9. Constraint Splitting and Projection Methodsfor Optimal Control

Yalcin Kaya (University of South Australia)


Heinz H. Bauschke, Regina S. Burachik and C. Yalcin

Kaya

We consider the minimum-energy control of a car,which is modelled as a point mass sliding on thefrictionless ground in a fixed direction, and soit can be mathematically described as the dou-ble integrator. The control variable, represent-ing the acceleration or the deceleration, is con-strained by simple bounds from above and below.Despite the simplicity of the problem, it is notpossible to find an analytical solution to it be-cause of the constrained control variable. To finda numerical solution to this problem we applythree different projection-type methods: (i) Dyk-stra’s algorithm, (ii) the Douglas–Rachford (DR)method and (iii) the Aragon Artacho–Campoy(AAC) algorithm. To our knowledge, these kindsof (projection) methods have not previously beenapplied to continuous-time optimal control prob-lems, which are infinite-dimensional optimizationproblems. The problem we study in this article isposed in infinite-dimensional Hilbert spaces. Be-haviour of the DR and AAC algorithms are ex-plored via numerical experiments with respect totheir parameters. An error analysis is also carriedout numerically for a particular instance of theproblem for each of the algorithms.

17.10. A variational approach to the Dubinstraveling salesman problem

David Kirszenblats (The University of Melbourne)


Mr David Kirszenblat

In this talk, we will propose a new method forsolving the Dubins traveling salesman problem,which asks for a shortest curvature-constrainedpath visiting an unordered set of locations in theplane. The problem is similar to the classicalEuclidean traveling salesman problem, which asksfor a shortest tour through a number of cities. Thedifference is that there is a curvature constraintthat accounts for the minimum turning radius ofa vehicle such as an unmanned aerial vehicle. Asa result, the problem contains elements of bothcontinuous and discrete geometric optimisation.Many heuristic approaches to the problem involve adiscretization of the configuration space, which canlead to a suboptimal solution. We propose a verydifferent approach, which draws inspiration froma mechanical model consisting of a string, pulleysand weights. Applying the calculus of variations,we derive optimality conditions to be satisfied by alocally shortest path. We then combine a gradient

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descent method with a branch and bound approachfor finding a globally shortest path.

17.11. Characterizations of Holder Error Bounds

Alexander Kruger (Federation University Australia)


Assoc Prof Alexander Kruger

We continue the study of necessary and sufficientsubdifferential conditions for Holder error bounds,particularly merging the conventional approachwith the new advancements proposed recently inYao, Zheng (2016). We formulate a general lemmacollecting the main arguments used in the proofsof the subdifferential sufficient error bound condi-tions and demonstrate that both linear and Holdertype conditions, conventional and the new advance-ments, can be obtained as direct consequences ofthis lemma. Some new estimates for the modulusof Holder error bounds will be presented.

17.12. A crash course on stability in linearoptimization

Marco Antonio Lopez Cerda (Alicante University)


Prof Marco Antonio Lopez Cerda

The talk is intended to provide a kind of biased sur-vey of our more representative results on stabilityfor the linear optimization problem. Qualitativeand quantitative approaches are both considered,and some infinite dimensional extensions of themain results are also presented. The material ofthis talk deals with the lower/upper semicontinu-ity of the feasible/optimal set mappings, differenttypes of ill-posedness, distance to ill-posedness,Lipschitz properties of these mappings under dif-ferent types of perturbations, and estimates of theassociated Lipschitz bounds.

17.13. Calculus of Kurdyka-Lojasiewicz exponentand its applications to sparse optimisation

Guoyin Li (University of New South Wales)


Dr Guoyin Li and Dr. Tingkei Pong

Nowadays, optimisation involving data of hugesizes is ubiquitous. Sparse optimisation hasemerged as a challenging frontier of modern optimi-sation because it effectively computes an optimalsolution with desired low complexity structure sothat a resulting solution can be efficiently stored,implemented and utilised, and is robust to thedata inexactness. Among many available methods,first-order methods and their acceleration counter-part are popular methods due to its simplicity andefficiency.

In this talk, we study the Kurdyka-Lojasiewicz(KL) exponent, an important quantity for analysing

the convergence rate of first-order methods. Specif-ically, we show that many convex or nonconvexoptimisation models that arise in applications suchas sparse recovery have objectives whose KL expo-nent is 1/2: this indicates that various first-ordermethods are locally linearly convergent when ap-plied to these models. Our results cover the sparselogistic regression problem and the least squaresproblem with SCAD or MCP regularization. Weachieve this by relating the KL inequality with anerror bound concept due to Luo and Tseng (1992),and developing calculus rules for the KL exponent.

17.14. Minimizing Equipment Shutdowns in Oiland Gas Campaign Maintenance

Ryan Loxton (Curtin University)


Ryan Loxton, Zeinab Seif, Elham Mardaneh

This talk considers the problem of scheduling peri-odic maintenance tasks in oil and gas plants. Themaintenance requirements are defined by a setof maintenance items, which are essentially listsof activities that may require costly equipmentshutdowns and isolations to complete. The aim isto minimize shutdowns by synchronizing mainte-nance items with similar shutdown requirementsinto short-term maintenance operations called cam-paigns. Real process plants can involve tens ofthousands of maintenance items and thus manu-ally scheduling the campaigns is extremely tedious.We describe a mixed-integer linear programmingmodel for optimally allocating maintenance itemsto campaigns so that total shutdown cost is min-imized. The model incorporates constraints onmaintenance deadlines, campaign times, mainte-nance item suppression and labour hours per cam-paign. The model has been tested on realisticscenarios for Karratha Gas Plant in Western Aus-tralia, which is the main processing plant for themassive North West Shelf oil and gas project.

17.15. Multi-objective Optimal Control Problems inBiomedical Engineering

Helmut Maurer (University of Mnster)


Yalcin Kaya, Helmut Maurer

In recent years, optimal control theory has beensuccessfully applied to various dynamic modelsin biomedical engineering. The choice of a sin-gle objective functional is a critical issue, since inmost cases we have to deal with competing ob-jectives. We consider dynamic systems that mayalso contain time delays in state and control vari-ables. When two or more objectives are given,we compute the efficient set (Pareto front) usinga Tschebycheff type approach. From a practicalpoint of view, it is often compulsory to choose asolution with an additional objective in mind. We

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sketch a method to carry out the optimization overthe efficient set. The multi-objective approach isillustrated on a combination therapy of cancer anda model of optimal vaccination and treatment inan epidemiological SEIR model. The same tech-niques can be applied to the optimal control of atime-delayed HIV model.

17.16. Nonlinear parametric error bounds

Cuong Nguyen Duys (Federation University

Australia)


Mr Nguyen Duy Cuong

Error bounds play an important role in sensitivityanalysis and convergence analysis of computationalalgorithms. In some cases, it is useful to study gen-eral nonlinear error bounds when the conventionallinear error bounds do not hold. In this talk, wediscuss a nonlinear parametric error bound modelfor lower semicontinuous functions in metric orBanach/Asplund spaces and provide some basictools to study this property. As applications, wewill show that nonlinear parametric error boundscan be used to establish necessary and/or sufficientconditions for nonlinear (graph) regularity prop-erties of set-valued mappings as well as nonlineartransversality properties of collections of sets.

17.17. Multi-objective mixed integer programming:An exact algorithm

William Erik Pettersson (University of Glasgow)


Dr William Erik Pettersson

Many heuristic methods have been used to findnon-dominated objective vectors to a multi-objectivemixed integer program (MOMIP), but no genericexact algorithms yet exist. The first exact algo-rithm for the bi-objective case was only given in2016. We present here an exact MOMIP algorithmthat generalises to an arbitrary number of objectivefunctions, the first such algorithm. Working withan arbitrary number of objective functions, say k,is particularly difficult as the set of non-dominatedobjective vectors consists of not necessarily con-vex polytopes of arbitrary dimension (up to k).Our new algorithm consists of three phases: (1)a collection phase, in which the algorithm findsall polytopes which contain some part of the solu-tion, (2) a convexity phase, which takes all suchpolytopes and creates a set of non-intersecting con-vex polytopes which cover the same set, and (3) adominance phase, which then compares such poly-topes to determine where (in the objective space)some polytopes may be either partially or totallydominated.

These three phases are presented so as to encouragefurther work to improve the performance of thealgorithm, and a Python implementation currently

in use for computational experiments will soon bemade available for use by other researchers.

17.18. Optimal Control on Unbounded Intervals -Fourier-Laguerre Analysis of the Problem

Sabine Pickenhain (Brandenburg Technical

University Cottbus)


Prof Sabine Pickenhain

We consider a class of infinite horizon variationaland control problems arising from economics, quan-tum mechanics and stabilization. Herein weassume that the objective is of regulator type.The problem setting implies uniformly and non-uniformly weighted Sobolev spaces as the statespaces. For this class of problems we use a dualityconcept of convex analysis to find sufficient opti-mality conditions. We develop a Fourier-Laguerremethod to solve the dual problem in an Hilbertspace setting.

17.19. A Derivative-free VU-algorithm for ConvexFunctions

Chayne Planiden (University of Wollongong)


Dr Chayne Planiden

The VU-algorithm is a two-step proximal bundlemethod that minimizes nonsmooth functions in asuperlinearly convergent manner. It takes advan-tage of the fact that the space can be separated intoa V-space, on which the objective function is non-smooth, and the orthogonal U-space, on which thefunction behaves smoothly. The proximal bundlemethod is used to take a minimizing step parallelto the V-space, then a quasi-Newton step can betaken parallel to the U-space, thus speeding upconvergence.

This work is our effort to create a derivative-freeversion of the VU-algorithm. Both the U-step andthe V-step rely on availability of gradients andHessians; we replace them with suitable approxi-mations via the simplex gradient and the minimumFrobenius norm. A novel tilt-correct step is intro-duced, in order to deal with the first-order errorin the proximal step. Convergence is proved andnumerical results are presented.

17.20. Electrical impedance tomography forunknown domains

Janosch Rieger (Monash University)


Dr Janosch Rieger, Prof Dr Bastian Harrach

Electrical impedance tomography is a noninvasiveimaging technique, which recovers the internalstructure of an object from the impact of externallyapplied electrical currents on its electrical potential.As this problem is strongly ill-posed, we do not

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17. Optimisation

attempt to solve it in its original form, but wecompute the convex source support introducedby Kusiak and Sylvester, which is a convex setcarrying useful information on the existence andthe approximate location of inhomogeneities in theimaged body.

In a first attempt, we computed the convex sourcesupport from a single measurement under the as-sumption that the exact shape of the imaged bodyis known and that the electrical potential can bemeasured on the entire boundary of the body. Inthis talk, I will present a local version of this ap-proach, in which we drop these assumptions almostentirely, which is an important step towards real-world applicability of the method. As before, wecompute the convex source support as the solutionof a shape optimisation problem, which we projectonto a suitable space of convex polytopes.

17.21. Reducing post-surgery recovery bedoccupancy through an analytical prediction model

Belinda Spratt (Queensland University of

Technology)


Dr Belinda Spratt, Prof Erhan Kozan

Operations Research approaches to surgical sched-uling are becoming increasingly popular in boththeory and practice. Often these models neglectstochasticity in order to reduce the computationalcomplexity of the problem. In this talk, historicaldata is used to examine the occupancy of post-surgery recovery spaces as a function of the initialsurgical case sequence. We show that the numberof patients in the recovery space is well modelledby a Poisson binomial random variable. A mixedinteger nonlinear programming model for the sur-gical case sequencing problem is presented thatreduces the maximum expected occupancy in post-surgery recovery spaces. Given the complexityof the problem, Simulated Annealing is used toproduce good solutions in short amounts of com-putational time. Computational experiments areperformed to compare the methodology here to afull year of historical data. The solution techniquespresented are able to reduce maximum expectedrecovery occupancy by 18% on average. This re-duction alleviates a large amount of stress on staffin the post-surgery recovery spaces and improvesthe quality of care provided to patients.

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18.1. The asymptotics of the large deviationprobabilities in the multivariate boundary crossingproblem

Kostya Borovkov (The University of Melbourne)


Prof Kostya Borovkov

For a multivariate random walk with i.i.d. jumpssatisfying the Cramer moment condition and hav-ing mean vector with at least one negative com-ponent, we derive the exact asymptotics of theprobability of ever hitting the positive orthantthat is being translated to infinity along a fixedvector with positive components. This setup ismotivated by a multivariate ruin problem. Ourapproach combines advanced large deviation tech-niques developed by A. Borovkov and A. Mogulskiiwith new auxiliary constructions, which enable usto extend their results on hitting remote sets withsmooth boundaries to the case of boundaries witha “corner” at the “most probable hitting point”.We also discuss how our results can be extendedto the case of more general target sets and to con-tinuous time Levy processes. [Joint work withY. Pan.]

18.2. Markov-modulated random walk searchstrategies for animal foraging

Lachlan James Bridgess (The University of

Adelaide)


Mr Lachlan James Bridges

Due to natural selection, it is hypothesised thata foraging animal should utilise a search strategythat is close to the theoretical optimal strategy.Thus, determining the theoretical optimal searchstrategy for a foraging animal is of practical usein the fields of ecology and conservation biology.Early animal foraging models found that a Levywalk optimised the search efficiency, and empiricalevidence for Levy walk strategies was found for anumber of different animal species. However, morerecent results have found that various intermittentsearch strategies can outperform a standard Levywalk. We will generalise these intermittent strate-gies in one dimension using Markov-modulatedrandom walks.

18.3. Long-term concentration of measure and thecut-off phenomenon

Graham Brightwell (London School of Economics)


Prof Graham Brightwell

We present concentration of measure inequalitiesfor Markov chains possessing a contractive cou-pling. We also illustrate the use of our inequalitiesto show that certain chains exhibit the cut-off phe-nomenon: the total variation distance between thedistributon of the chain at time t and the station-ary distribution drops from 1 to 0 over a shorttime interval. (Joint work with Andrew Barbourand Malwina Luczak.)

18.4. Sampling via Regenerative Chain Monte Carlo

Yi-Lung Chens (University of New South Wales)


Mx Yi-Lung Chen

MCMC techniques are popular solutions to ap-proximate quantities that are difficult to computeexactly. Unfortunately, despite its wide use acrossvarious fields, most Markov chain samplers lacktheoretically justified methods to analyze their out-put. That is to say, most MCMC samplers lacka) a consistent variance estimator for a given er-godic average; and b) an estimator for the totalvariation distance between the distribution of adraw from the Markov chain sampler and its targetdistribution.

In this study, we take a Gibbs sampler for theposterior distribution of the Bayesian Lasso asan example, and demonstrate how one can sys-tematically address a) and b) by exploiting theunderlying regenerative structure of the simulationoutput. Roughly speaking, regenerative structureare the times when a stochastic process (in thiscase a Markov chain) scholastically ‘restarts’ itself.Intuitively, if a Markov chain frequently ‘restarts’itself, it should have a fast convergence hence, onemay examine the convergence of a Markov chainsampler by identifying these events. Note thathowever a drawback of the proposed methodologyis that it primarily applies to models, which whileintractable, exhibit a lot of structure and permitanalytical approximations.

18.5. Statistical Uncertainty in Decision Making

Samuel Cohen (The University of Oxford)


Assoc Prof Samuel Cohen

Much work in mathematical finance has revolvedaround how to incorporate an understanding of‘Knightian’ uncertainty in valuations. Largely, thishas been done with little attention to statistics.In this talk we shall consider how uncertainty inestimation can be explicitly and consistently incor-porated in valuation of decisions, using the theoryof nonlinear expectations.

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18.6. Branching ruin number

Andrea Collevecchio (Monash University)


Dr Andrea Collevecchio

The branching-ruin number of a tree, which de-scribes its asymptotic growth and geometry, can beseen as a polynomial version of the branching num-ber. This quantity was defined by Collevecchio,Kious and Sidoravicius (2018) in order to under-stand the phase transitions of the once-reinforcedrandom walk (ORRW) on trees. Strikingly, thisnumber was proved to be equal to the criticalparameter of the ORRW on trees. In this talk,we present new results on the link between thebranching-ruin number and the criticality of ran-dom processes on trees. First, we study ran-dom walks on random conductances on trees,when the conductances have an heavy tail at zero,parametrized by some p > 1, where 1/p is theexponent of the tail. We prove a phase transi-tion recurrence/transience with respect to p andidentify the critical parameter to be equal to thebranching-ruin number of the tree. Second, westudy a multi-excited random walk on trees whereeach vertex has M cookies and each cookie hasan infinite strength towards the root. Here again,we prove a phase transition recurrence/transienceand identify the critical number of cookies to beequal to the branching-ruin number of the tree,minus 1. This result extends a conjecture of Volkov(2003). Besides, we study a generalized version ofthis process and generalize results of Basdevantand Singh (2009). Based on joint work with CongBang Huynh and Daniel Kious

18.7. Directed walk on a randomly oriented lattice

Kais Hamza (Monash University)


Assoc Prof Kais Hamza

Consider a randomly-oriented Manhattan lattice,where every line in Z2 is assigned, once and forall, a random direction by flipping independentfair coins. At each step, the particle moves to thenearest site along the diagonal in the direction ofthe line orientations at the current site. We provethat the walk thus defined localizes on two verticesat all large times, almost surely. We also provideestimates for the tail of the length of paths. Inparticular, we show that the probability of thepath to be larger than n decays sub-exponentiallyin n.

Joint work with Andrea Collevecchio and LaurentTournier.

18.8. Central limit theorems for dynamic randomgraph models

Liam Hodgkinsons (University of Queensland)


Mr Liam Hodgkinson

Perhaps the most common representation of a com-plex network is that of a random graph of largesize. There is a significant body of work devotedto analysing large dense random graphs, usuallythrough their homomorphism densities, that is, theproportion of appearances of a chosen shape (trian-gles, for example). Unfortunately, there has beenless success in analysing dynamic (time-evolving)random graph models. In this talk, I will considera class of discrete-time Markov dynamic randomgraph models evolving as inhomogeneous randomgraphs with edge probabilities depending on theprevious state. Under suitable assumptions, I willshow how one can prove central limit theorems fortheir homomorphism densities.

18.9. The power of QED-like scaling formany-server queues in a random environment

Hermanus Marinus Jansen (The University of

Queensland)


Mr Hermanus Marinus Jansen

We consider a many-server queue whose param-eters are modulated by an independent right-continuous stochastic process (called the back-ground process). This means that the arrival rateand the server speed both depend on the stateof the background process. We are interested indiffusion limits for this type of queue and espe-cially in the influence of the background processon the limit. We show that a diffusion limit existsunder quite general scaling conditions. Both thescaling and the limit depend on the second orderbehaviour of the background process in this case.However, generalising the QED or Halfin-Whittscaling to modulated queues, we see that in thisspecial case neither the scaling nor the diffusionlimit depends on the second order behaviour ofthe background process. This suggest that a naveQED-like scaling is actually a good way to dealwith a random environment, in that the systembecomes insensitive for fluctuations of the back-ground process.

18.10. Algorithms for Markovian Regime Switching(MRS) models for electricity prices

Angus Hamilton Lewiss (The University of

Adelaide)


Mr Angus Hamilton Lewis

A popular model for electricity prices is theindependent-regime MRS model whereby multiple

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independent AR(1) processes are interweaved by aMarkov Chain. These models can be viewed as anextension of Hidden Markov models (HMMs) orregime-switching time series. We can think of thesemodels as multiple independent AR(1) processesevolving, but at each time we only observe one ofthem, and which process is observed is determinedby a (hidden) Markov chain. In this talk, we ex-tend the classical forward-backward algorithm forHMMs to this model, which allows us to evaluatethe likelihood, implement the EM algorithm andfind the MLEs for these models. These resultsare presented in the context of electricity pricemodelling.

18.11. Perfect Sampling for Gibbs Point Processesusing Partial Rejection Sampling

Sarat Babu Moka (The University of Queensland)


Dr Sarat Babu Moka

We present a perfect sampling algorithm for Gibbspoint processes, based on the partial rejection sam-pling of Guo et al. (2017). We focus on pairwiseinteraction processes and penetrable spheres mixedmodels; examples include hard-core, Strauss andarea-interaction processes. Given that the interac-tion range of the target process is r, the proposedalgorithm has O(log(1/r)) running time complex-ity for generating a perfect sample, provided thatthe density of the points is not too high.

18.12. Correlated time-changed Levy processes

Kihun Nam (Monash University)


Dr. Hasan Fallahgoul and Dr Kihun Nam

Time-changed Levy processes, which consist ofa Levy process that runs on a stochastic time,can effectively capture main empirical regulari-ties of asset returns such as jumps, stochasticvolatility, and leverage. However, neither theirtransitional density nor characteristic function isavailable in closed-form when the Levy processand time-change are not independent. For a givensolution to a linear parabolic partial differentialequation, we derive a closed-form expression for thetransitional density, moment generating function,and characteristic function of the time-changedLevy processes, when the Levy and time-changeprocess are correlated. Our approach can be ap-plied to virtually all models in the option pricingliterature. This is a joint work with Dr. HasanFallahgoul.

18.13. Statistics and filter transforms ofGegenbauer-type processes

Andriy Olenko (La Trobe University)


Dr Andriy Olenko

General filter transforms of stochastic processesare studied. As a particular case these transforma-tions include wavelet transformations. They areapplied to Gegenbauer-type seasonal long-memoryprocesses with spectral singularities outside theorigin. Estimates for the singularity location andlong-memory parameters are proposed. Their al-most surely convergence to the true values of pa-rameters is proved. Solutions of the estimationequations are studied and adjusted statistics areproposes. Numerical results are presented to con-firm the theoretical findings.

The talk is based on joint results with H. Alomari(La Trobe University, Australia), A. Ayache andM. Fradon (University of Lille, France).

18.14. A fluid flow model with RAP components

Oscar Peraltas (Technical University of Denmark)


N. Bean, G. Nguyen, B. F. Nielsen, and O. Peralta

The class of matrix-exponential distributions (ME)constitutes an algebraic generalisation of the classof phase-type distributions (PH). Similarly, theRational arrival process (RAP) generalises theMarkovian arrival process (MAP) in an algebraicsense, however, their probabilistic constructionsare considerably different. For the MAP, the driv-ing process is a Markov jump process with finitestate space, while it is a piecewise deterministicMarkov process (PDMP) for the RAP. This ap-proach has been further studied in the literatureto define a class of quasi-birth and death processes(QBD) with RAP components, an algebraic gen-eralisation of the QBD. In this talk we provide ageneralisation of the fluid flow model in a similardirection. More specifically, we construct a Markovadditive process with an underlying PDMP whosecharacteristics are similar to the one associatedto the RAP, which we call Fluid RAP (FRAP).We analyse some first passage probabilities of theFRAP, which are shown to be algebraic extensionsof classic results for the fluid flow model. We con-clude by discussing the similarities and differencesbetween the techniques that were needed to studythe FRAP and the ones commonly used for fluidflow models in the literature.

18.15. Why is Kemeny’s constant a constant?

Peter Taylor (The University of Melbourne)


Peter Taylor, with Dario Bini, Jeff Hunter, Guy

Latouche and Beatrice Meini

In their 1960 book on finite Markov chains, Ke-meny and Snell established that a certain sumis invariant. The value of this sum has becomeknown as Kemeny’s constant. Various proofs forthe invariance have been given over time, somemore technical than others. We shall first give a

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simple algebraic proof and then follow it up with aprobabilistic proof that gives physical insight intowhat is going on. The result extends without ahitch to continuous-time Markov chains on a finitestate space.

For Markov chains with denumerably infinite statespace, the constant may be infinite and even if itis finite, there is no guarantee that the physical ar-gument will hold. We shall show that the physicalinterpretation does go through for the special caseof a birth-and-death process with a finite value ofKemeny’s constant.

18.16. On asymptotic behavior of weightedfunctionals of long-range dependent random fieldson spheres

Volodymyr Vaskovychs (La Trobe University)


Mr Volodymyr Vaskovych

We study long-range dependent random fields de-fined on the sphere. The asymptotic behaviorof the least-squares estimator in the regressionmodel with the error given by such fields is inves-tigated. The least-squares estimator in this modelis a weighted functional of random fields with long-range dependence. It is known that in this scenariothe limits can be non-Gaussian. We obtain thelimiting distribution and the rate of convergencefor these functionals. The results were obtainedunder rather general assumptions on the spectraldensities of the random fields. Some simulationstudies are presented to support theoretical find-ings. This is a joint work with V. Anh (QUT),and A. Olenko (La Trobe University).

[1]V. Anh, A. Olenko, V. Vaskovych, On LSE inregression model for long-range dependent randomfields on spheres, submitted.

18.17. Stochastic networks with selfish routing andinformation feedback

Ilze Ziedins (The University of Auckland)


Assoc Prof Ilze Ziedins

There are many networks where individuals choosewhich route to take to minimize their own delay(selfish routing), and in some cases may even choosenot to enter the network at all (balking or reneg-ing). We will compare and contrast behaviour intwo different kinds of network — parallel queues,and linear networks with feedback. In the former,individuals choose which queue to enter, and prob-abilistic and state-dependent routing can give verydifferent behaviours. In the latter, feedback op-erates to deter users from entering the system asdelays increase. The linear system also has a ratecontrol on entries to the system, and the interac-tion between this and the state-dependent arrivalrate are of particular interest. Both models are

idealized versions of traffic models — the parallelqueues model private vs. public transport routes,the linear network models a motorway with rampmetering.

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19.1. The Selberg integral and Macdonaldpolynomials

Seamus Albions (The University of Queensland)


Mr Seamus Albion

In 1944, Atle Selberg discovered a remarkable gen-eralisation of Euler’s beta integral. Now known asthe Selberg integral, it has since played an impor-tant role in analytic number theory, random matrixtheory, and conformal field theory. In their recentproof of the AGT conjecture for SU(2), Alba, Fa-teev, Litvinov, and Tarnopolsky (2011) required aSelberg integral over a pair of Jack polynomials. Inthis talk we will discuss how to obtain the integralof Alba et al. using Macdonald polynomial theoryas well as some further generalisations for SU(n).

19.2. Recollement of perverse sheaves on realhyperplane arrangements

Asilata Bapat (Australian National University)


Dr Asilata Bapat

A hyperplane arrangement gives a stratification ona vector space, whose topology is encoded in an as-sociated abelian category of perverse sheaves. Theinterplay between the perverse sheaves and theirrestrictions to the open and closed strata is knownas recollement. The category of perverse sheavesassociated to a hyperplane arrangement has analternate algebraic description due to Kapranovand Schechtman. In this talk, I will describe rec-ollement in terms of this algebraic interpretation.I will also briefly discuss the special case of finiteCoxeter arrangements, building on work by MartinWeissman.

19.3. Quantum polynomial functors

Valentin Buciumas (The University of Queensland)


Dr Valentin Buciumas

The classical polynomial functors of Friedlanderand Suslin give a useful interpretation of the poly-nomial representation theory of the general lineargroup. I will present a quantum generalization ofthe category of polynomial functors and explainwhat is needed to generalize two properties of poly-nomial functors: stability and composition. Timepermitting, I will talk about a quantum ‘type BCD’generalization of polynomial functors. This is jointwork with Hankyung Ko.

19.4. Finite dimensional representations oforthosymplectic supergroups

Michael Ehrig (The University of Sydney)


Dr Michael Ehrig

In the talk I want to review how to obtain a descrip-tion of the category of finite dimensional represen-tations for the orthosymplectic supergroup via agraded version of the Deligne category and associ-ated Brauer algebra. This is joint with CatharinaStroppel.

19.5. p-groups related to exceptional Chevalleygroups

Saul Freedmans (The University of Western

Australia)


Mr Saul D. Freedman

It is well-known that given any finite group, we canuse standard representation theory to representthe group on some finite vector space, i.e., on someelementary abelian p-group. In 1978, Bryant andKovacs proved an analogue of this fact for p-groupsthat are not elementary abelian. Namely, if H isa subgroup of the general linear group GL(d, p),with d > 1, then there exists a p-group P such thatAut(P ) induces H on the Frattini quotient of P .However, it is not known in general when we canchoose P to be small, in terms of its exponent-pclass, exponent, nilpotency class and order. Inthis talk, we consider the representation theoryof the (finite) simply connected versions of theexceptional Chevalley groups, and their overgroupsin corresponding general linear groups, in order toconstruct small related p-groups.

19.6. The Product Monomial Crystal

Joel Gibsons (The University of Sydney)


Joel Gibson

The product monomial crystal is the non-genericcase of Nakajima’s tensor product crystals for asemisimple Lie algebra. In this talk I present aDemazure-type character formula for these crys-tals. In type A, this character formula shows thatthe product monomial crystal corresponds to thegeneralised Schur module, a family of GLn mod-ules which generalise irreducibles and skew-Schurmodules.

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19.7. A Soergel-like category for complex reflectiongroups of rank one

Thomas Gobet (The University of Sydney)


Dr Thomas Gobet

We introduce analogues of Soergel bimodules forcomplex reflection groups of rank one. We describethe indecomposable objects in the category andgive a presentation by generators and relationsof its split Grothendieck ring. This ring turnsout to be an extension of the Hecke algebra ofthe reflection group, and is generically semisimple(when defined over the complex numbers).

This is joint work with Anne-Laure Thiel.

19.8. Puzzles for restricting Schubert classes to thesymplectic Grassmannian

Iva Halacheva (The University of Melbourne)


Ms Iva Halacheva

The Grassmannian Gr(k,V) of k-planes in a sym-plectic vector space V contains the subschemeSpGr(k,V) of k-planes which are self-orthogonal.Using the pullback along the inclusion map, a nat-ural question is to consider how the image of aSchubert class of Gr(k,V) expands into Schubertclasses of SpGr(k,V). Coskun gave an algorithmfor positively computing this in cohomology. Weuse puzzles and techniques from integrable systemsto generalize this result to equivariant cohomologyand K-theory.

19.9. Complementary symmetry for Slodowyvarieties

Anthony Henderson (The University of Sydney)


Prof Anthony Henderson

Let λ and µ be two partitions with the first domi-nating the second. Various quantities f(λ, µ) at-tached to such a pair obey a rule of ‘complementarysymmetry’: if λc and µc denote the partitions ob-tained by taking the diagrams complementary tothose of λ and µ in a fixed rectangle and rotatingthem 180 degrees, then f(λc, µc) = f(λ, µ). Forexample, this holds for the Kostka number Kλ,µ.I will discuss a geometric result along these lines,stating that Slodowy varieties for the general lineargroup obey this complementary symmetry, whichhas recently been generalized to other classicalgroups by Yiqiang Li.

19.10. Braid group action on triangulatedcategories

Edmund Xian Chen Hengs (Australian National

University)


Mr Edmund Xian Chen Heng

It is known that braid groups act on the curves ofpunctured disk and through this, Thurston gavea classification theory of braid groups by lookingat the dynamics of this action. By a paper writ-ten by Khovanov and Seidel, these curves on thepunctured disk can be viewed as objects in thehomotopy category of bounded chain complexes ofprojective modules over the zig-zag algebra. Fur-thermore, the braid group acts on it just as howit acts on curves. In this talk I will describe therecipe to relate the geometrical objects (curves)to the algebraic objects (complexes) and how thisgives us an action on a triangulated category.

19.11. Topology of representation stacks

Masoud Kamgarpour (University of Queensland)


Dr Masoud Kamgarpour

I will talk about computing how to compute theEuler characteristic of the stack of finite dimen-sional representations of the fundamental group ofRiemann surface. This is joint work with DavidBaraglia.

19.12. Inner products on graded Specht modules

Alexander Ferdinand Kerschls (The University of

Sydney)


Mr Alexander Ferdinand Kerschl

A cellular basis of an algebra gives a natural wayof constructing “cell modules” for the algebra, thatcome equipped with an associative inner product.Quotiening out by the radical of the inner prod-ucts on the cell modules gives a complete set ofpairwise non-isomorphic simple modules for thealgebra. Webster introduced a diagrammatic al-gebra, the diagramatic Cherednik algebra, thatcontains the much studied quiver Hecke algebra oftype A as a sub-algebra. Building on Webster’swork, Bowman constructed several graded cellu-lar bases for the quiver Hecke algebras using thediagrams that depend on a loading θ. We use Web-ster’s diagram calculus and the theory of cellularalgebras to compute inner products of particularbasis elements in corresponding cell modules, thegraded Specht modules. As an application weclassify the simple modules for the quiver Heckealgebras in terms of the loading. We also obtainresults on graded dimensions of the simple modulesof these algebras.

19.13. The p-Part of the Order of an AlmostSimple Group of Lie Type

Marvin Kringss (RWTH Aachen University)


S.P. Glasby, Marvin Krings, Alice C. Niemeyer

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Primitive permutation groups are fundamentalbuilding blocks in the sense that every finite per-mutation group can be built from the primitiveones. Apart from the alternating group An andthe symmetric group Sn of degree n, the primi-tive subgroups G of Sn are small. For example,in 1980 Praeger and Saxl showed that |G| ≤ 4n,which is much smaller than n!

2 . Since this time,powerful results such as the O’Nan-Scott Theorem,which classifies the primitive permutation groups,and the Classification of the Finite Simple Groups,have become available.

We will bound the p-part |G|p of |G| for some

prime p. This is the largest p-power pνp(G) thatdivides |G|. The bound |G| ≤ 4n implies νp(G) ≤n logp(4). We prove the stronger bound νp(G) ≤2√n

(p−1) + 1 (with five exceptions). For several cases,

we even obtain a bound that is logarithmic in n.

Our proof uses the O’Nan-Scott theorem to reduceto simple groups. The hardest case, and the oneI will discuss, is when the simple group is of Lietype.

19.14. A product formula for certain coefficients ofMacdonald polynomials

Yusra Naqvi (The University of Sydney)


Dr Yusra Naqvi

Macdonald polynomials generalise several classi-cal families of symmetric polynomials, includingSchur polynomials, Jack polynomials and Hall-Littlewood polynomials. In 1989, Richard Stan-ley conjectured that certain coefficients obtainedwhen a product of Jack polynomials is expandedin the Jack basis can be expressed as a product ofweighted hooks of Young diagrams. In this talk,I will outline a proof of a special case of this con-jecture and its extension to the case of Macdonaldpolynomials.

19.15. An orbit model for the spectra of nilpotentGelfand pairs

Anna Romanov (The University of Sydney)


Dr Anna Romanov

Let N be a connected and simply connected nilpo-tent Lie group, and let K be a subgroup of theautomorphism group of N. We say that the pair(K,N) is a nilpotent Gelfand pair if the set of inte-grable K-invariant functions on N forms an abelianalgebra under convolution. In 2008, Benson andRacliff established a one-to-one correspondence be-tween the set of bounded K-spherical functions forsuch a Gelfand pair and a set of K-orbits in thedual of the Lie algebra of N. The sets on eitherside of this bijection can be given the structure of

topological spaces, and Benson and Ratcliff con-jectured that this set-theoretic correspondence isactually topological. In this talk, we will describeBenson-Racliff’s construction and provide a proofof their conjecture for a certain class of nilpotentGelfand pairs, establishing a geometric model forthe spectrum of such pairs. This is joint workwith H. Friedlander, W. Grodzicki, W. Johnson,G. Ratcliff, B. Strasser, and B. Wessel.

19.16. Crystal structures for symmetricGrothendieck polynomials

Travis Scrimshaw (The University of Queensland)


Dr Travis Scrimshaw

Kashiwara’s theory of crystal bases allows oneto study the representation theory of (Drinfel’d-Jimbo) quantum groups using combinatorics. Ithas a received significant attention since its incep-tion in the 1990s and has been connected to numer-ous fields of mathematics. One particular exampleof crystals is to semistandard Young tableaux fortype An irreducible representations, which hasgiven a representation theoretic explanation ofmany now classical combinatorial constructions.

Another well-studied object is the Grassmannian,the set of k-dimensional subspaces in n-dimensionalspace. Here, the Schubert classes in the cohomol-ogy are given by certain Schur functions, whichare the characters of the type An irreducible rep-resentations. For the K-theory of the Grassman-nian, the Schubert classes correspond to symmetricGrothendieck polynomials. In terms of combina-torics, they are known to be a sum over set-valuedtableaux and decompose positively (up to a signbased on the degree) in terms of Schur functions.

In this talk, we will show that set-valued tableauxhave a type An crystal structure, which recoversthe Schur function decomposition. We will alsodiscuss a potential K-theoretic extension of crys-tals. This is joint work with Cara Monical andOliver Pechenik.

19.17. Two models of equivariant ellipticcohomology

Matthew James Spongs (The University of

Melbourne)


Mx Matthew James Spong

In 1994, Grojnowski gave a construction of an equi-variant elliptic cohomology theory associated to anelliptic curve over the complex numbers. This hasseen useful applications in both algebraic topol-ogy and geometric representation theory, howeverthe construction is somewhat ad hoc and therehas been significant interest in the question of itsgeometric interpretation.

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We show that there are two global models for Gro-jnowski’s theory, which shed light on its geometricmeaning. One model is constructed as the loopgroup-equivariant K-theory of a free loop space.This is a slight modification of a construction whichwas given by Kitchloo in 2014, and our main contri-bution here is to determine its precise relationshipwith Grojnowski’s theory. The second model isconstructed as the Borel-equivariant cohomologyof a double free loop space. This is equivariantfor the action of the gauge group of the trivialprincipal bundle on an orientable genus 1 surface.This largely follows a proposal of Rezk from 2016.

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20. Public Lecture

20.1. The shape of our planet Earth: amathematical challenge!

Etienne Ghys (Ecole normale superieure de Lyon)


Prof Etienne Ghys

Our planet Earth is rotating. The centrifugal forceproduces some equatorial bulge so that the Earthis not exactly spherical. The mathematical ques-tion of the determination of the shape of a rotatingbody has been central in the development of math-ematics for several centuries. Newton was the firstto get an estimate of the flattening of the Earth bya purely theoretical reasoning, “without having toget out of his home”, as Voltaire wrote. I will dis-cuss historical developments, like for instance thesurprising discovery by Poincare of rotating bodieshaving the shape of a pear! This topic is indeed awonderful example of the interaction between pureand applied science. Even though the question hasbeen studied by the greatest mathematicians since350 years and many discoveries have been made,many important questions still remain open.

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List of Registrants

Current as of Sun 2 Dec 2018

Mr Remy Alexander Addertons The Australian National UniversityDr Zahra Afsar The University of SydneyMrs Shaymaa Shawkat Kadhim Al-shakarchisUniversity of New South WalesMr Seamus Albions The University of QueenslandDr Amie Albrecht University of South AustraliaMrs Faezeh Alizadehs Shahid Rajaee Teacher Training UniversityAssoc Prof Tansu Alpcan The University of MelbourneDr Ambily Ambattu Asokan Cochin University of Science and TechnologyMiss Becky Armstrongs The University of SydneyDr Romina Melisa Arroyo University of QueenslandMiss Ayreena Bakhtawars La Trobe UniversityDr John Banks The University of MelbourneDr Asilata Bapat Australian National UniversityDr David Baraglia The University of AdelaideMr Fawwaz Bataynehs University of QueenslandDr Nicholas Beaton The University of MelbourneMx Kimberly Beckers The University of AdelaideMr Theo Bendits The University of NewcastleProf Renato Ghini Bettiol City University of New YorkMr Alex Bishops University of Technology, SydneyMr Matteo Bordignons University of New South Wales CanberraProf Kostya Borovkov The University of MelbourneMr Philip Boss La Trobe UniversityAssoc Prof Murk Bottema Flinders UniversityMs Elizabeth Bradfords University of South AustraliaProf Florian Breuer The University of NewcastleMr Lachlan James Bridgess The University of AdelaideProf Graham Brightwell London School of EconomicsProf Philip Broadbridge La Trobe UniversityMr David Leonard Brooks The University of AdelaideDr Arnaud Brothier UNSW SydneyDr Nathan Brownlowe The University of SydneyDr Valentin Buciumas The University of QueenslandDr Anh Bui Macquarie UniversityMs Thi Hoa Buis Federation University AustraliaDr Judith Bunder The University of AdelaideAssoc Prof Regina Burachik University of South AustraliaProf Benjamin Burton University of QueenslandDr David Butler The University of AdelaideMr Timothy Peter Bywaterss The University of SydneyDr Grant Cairns La Trobe UniversityMiss Bethany Caldwells University of South AustraliaDr Alexander Campbell Macquarie UniversityProf Pietro Cerone La Trobe UniversityMr Anupam Chaudhuris Monash UniversityDr Mike Chen The University of AdelaideMx Yi-Lung Chens University of New South WalesMr Hanz Martin Chengs Monash UniversityDr Xing Cheng Monash University

111

List of Registrants

Prof Jeongwhan Choi Korea UniversityDr Renu Choudhary Auckland University of TechnologyDr Kieran Clancy Flinders UniversityDr Julie Clutterbuck Monash UniversityAssoc Prof Samuel Cohen The University of OxfordDr Andrea Collevecchio Monash UniversityDr Julia Collins Australian Mathematical Sciences InstituteMr Don Coutts Canberra Institute of TechnologyDr Peter Cudmore The University of MelbourneMs Michaela Cully-Hugills University of New South Wales CanberraMr Zhou Dais University of South AustraliaDr Zsuzsanna Dancso The University of SydneyDr Minh N. Dao The University of NewcastleProf Jan De Gier The University of MelbourneMr Raveen Daminda de Silvas University of New South WalesDr Owen Dearricott The University of MelbourneDr Anand Rajendra Deopurkar Australian National UniversityAssoc Prof Josef Dick University of New South WalesMr Neil Kristofer Dizons The University of NewcastleMr Hong Chuong Doans Macquarie UniversityDr Roland Dodd Central Queensland UniversityProf Diane Donovan The University of QueenslandMr Kumbu Dorjis University of New EnglandDr Ian Doust University of New South WalesProf Silvestru Sever Dragomir Victoria UniversityAssoc Prof Jerome Droniou Monash UniversityProf Xuan Duong Macquarie UniversityDr James East Western Sydney UniversityProf Michael Eastwood The University of AdelaideProf Andrew Craig Eberhard Royal Melbourne Institute of TechnologyDr Michael Ehrig The University of SydneyMr Andrei Ermakovs University of Southern QueenslandMr Nicholas Fewster-Young University of South AustraliaProf Jerzy Filar The University of QueenslandMr Keegan Floods The University of AucklandDr Chi-Kwong Fok The University of AdelaideProf Peter Forrester The University of MelbourneMiss Kelli Francis-Staites The University of OxfordMr Saul Freedmans The University of Western AustraliaProf Wilhelm Freire Universidade Federal de Juiz de ForaProf Vladimir Gaitsgory Macquarie UniversityMrs Ajini Galapitages University of South AustraliaMr Anthony John Gallos The University of AdelaideAssoc Prof Timothy Garoni Monash UniversityDr Alejandra Garrido The University of NewcastleDr David Gepner The University of MelbourneProf Etienne Ghys Ecole Normale superieure de LyonMr Joel Gibsons The University of SydneyProf Michael Giudici The University of Western AustraliaDr Stephen Glasby The University of Western AustraliaDr Wolfgang Globke University of ViennaDr David G Glynn Flinders UniversityDr Thomas Gobet The University of SydneyMr Yoong Kuan Gohs University of Technology, SydneyDr Cecilia Gonzalez-Tokman The University of QueenslandProf Joseph Grotowski The University of QueenslandDr Xing Gu AMSI/University of MelbourneDr Chen Guanheng The University of AdelaideDr Hailong Guo The University of Melbourne

112

List of Registrants

Prof William Guo Central Queensland UniversityMs Iva Halacheva The University of MelbourneMr Michael Alexander Hallams The University of AdelaideMs Sophie Hams Monash UniversityAssoc Prof Kais Hamza Monash UniversityAssoc Prof Fei Han National University of SingaporeDr David Hartley University of WollongongDr Michael Haythorpe Flinders UniversityProf Roozbeh Hazrat Western Sydney UniversityDr Jian He Monash UniversityProf Markus Hegland Australian National UniversityDr Pedram Hekmati The University of AucklandProf Anthony Henderson The University of SydneyMr Edmund Xian Chen Hengs Australian National UniversityDr Peter Hochs The University of AdelaideMr Liam Hodgkinsons University of QueenslandDr Algy Howe Australian National UniversityProf Phil Howlett University of South AustraliaDr Melissa Humphries The University of AdelaideDr Mumtaz Hussain La Trobe UniversityDr Deborah Jackson La Trobe UniversityMiss Sarah Jamess The University of AdelaideDr Simon James Deakin UniversityMr Hermanus Marinus Jansen The University of QueenslandDr Iwan Jensen Flinders UniversityMr Daniel Johns The University of AdelaideProf Nalini Joshi The University of SydneyDr Zlatko Jovanoski University of New South Wales CanberraProf Kenji Kajiwara Kyushu UniversityDr Masoud Kamgarpour University of QueenslandDr Sevvandi Priyanvada Kandanaarachchi Monash UniversityDr Yalcin Kaya University of South AustraliaMs Carolyn Kennett Macquarie UniversityMr Alexander Ferdinand Kerschls The University of SydneyDr Tran Vu Khanh University of WollongongDr Carlisle King The University of Western AustraliaAssoc Prof Deborah King The University of MelbourneMr David Kirszenblats The University of MelbourneMiss Maria Kleshninas The University of QueenslandDr Krzysztof Krakowski Cardinal Stefan Wyszynski University in WarsawAssoc Prof Jonathan Kress University of New South WalesMr Marvin Kringss RWTH Aachen UniversityProf Manjunath Krishnapur Indian Institute of Science BangaloreAssoc Prof Alexander Kruger Federation University AustraliaDr Neeraj Kumars IIT BombayDr Kwok-Kun Kwong The University of SydneyDr Ramiro Augusto Lafuente The University of QueenslandProf Marco Antonio Lopez Cerda Alicante UniversityDr Quoc Thong Le Gia University of New South WalesDr Thomas Leistner The University of AdelaideMr Renaud Leplaideur Universite de la Nouvelle CaledonieMr Angus Hamilton Lewiss The University of AdelaideAssoc Prof Guoyin Li University of New South WalesDr Joan Licata Australian National UniversityMr Johnny Lims The University of AdelaideDr Boris Lishak The University of SydneyMr Dennis Lius The University of AdelaideMiss Xuemei Lius University of South AustraliaDr Heather Lonsdale Curtin University

113

List of Registrants

Prof John Loxton Western Sydney UniversityProf Ryan Loxton Curtin UniversityProf Malwina Luczak The University of MelbourneDr Matthias Ludewig The University of AdelaideMr Yuki Maeharas Macquarie UniversityDr Chi Mak University of New South WalesMr Benjamin Maldons The University of NewcastleMr Michael Arthur Mampustis University of WollongongDr Daniel Francis Mansfield University of New South WalesDr Robert Marangell The University of SydneyMr Anthony Shane Marshalls Flinders UniversityDr Margaret Marshman University of the Sunshine CoastProf Helmut Maurer University of MnsterDr Anthony Mays The University of MelbourneAssoc Prof James McCoy The University of NewcastleDr Robert McDougall University of the Sunshine CoastProf Mark Joseph McGuinness Victoria University of WellingtonAssoc Prof William McLean University of New South WalesDr Peter McNamara The University of MelbourneMr Samuel Millss The University of AdelaideMs Stephanie Millss University of South AustraliaDr Lewis Mitchell The University of AdelaideDr Sarat Babu Moka The University of QueenslandMr Benjamin Moores The University of AdelaideDr Ross Moore Macquarie UniversityDr Luke Morgan The University of Western AustraliaDr Thomas Morrill UNSW CanberraProf Sid Morris Federation University AustraliaMiss Jessica Murphys The University of SydneyProf Michael Murray The University of AdelaideDr Kihun Nam Monash UniversityDr Yusra Naqvi The University of SydneyAssoc Prof Mark Nelson University of WollongongMr Alex Newcombes Flinders UniversityDr Garry Newsam The University of AdelaideDr Giang Nguyen The University of AdelaideMs Trang Nguyens University of South AustraliaMr Cuong Nguyen Duys Federation University AustraliaDr Yuri Nikolayevsky La Trobe UniversityDr Greg Oates University of TasmaniaDr Andriy Olenko La Trobe UniversityProf Hinke Osinga The University of AucklandDr Alessandro Ottazzi University of New South WalesDr Brett Parker Monash UniversityMr Thomas Pedersens University of WollongongMr Oscar Peraltas Technical University of DenmarkDr William Erik Pettersson University of GlasgowProf Sabine Pickenhain Brandenburg Technical University CottbusDr Chayne Planiden University of WollongongAssoc Prof Jessica Purcell Monash UniversityDr Thomas Quella The University of MelbourneProf Reinout Quispel La Trobe UniversityProf Chris Radford Memorial UniversityDr Nawin Raj University of Southern QueenslandMx Jacqui Ramagge The University of SydneyDr Colin David Reid The University of NewcastleDr Janosch Rieger Monash UniversityDr David Roberts The University of AdelaideMr Timothy Robertss The University of Sydney

114

List of Registrants

Dr David Robertson The University of NewcastleDr Marcy Robertson The University of MelbourneDr Vanessa Robins Australian National UniversityDr Anna Romanov The University of SydneyDr Danya Rose The University of SydneyDr Joshua Ross The University of AdelaideMr Matthew James Ryans The University of AdelaideMr Thomas Scheckters University of New South WalesProf Gerd Schmalz University of New EnglandDr Jelena Schmalz University of New EnglandDr Travis Scrimshaw The University of QueenslandMr Nicholas Seatons University of WollongongDr Min Sha Macquarie UniversityProf Nageswari Shanmugalingam University of CincinnatiMr Yibing Shens The University of QueenslandProf Steven Sherwood University of New South WalesMs Yang Shi Flinders UniversityProf Harvinder Sidhu University of New South WalesDr Leesa Sidhu University of New South Wales CanberraProf Miles Simon Magdeburg UniversityProf Michael Small The University of Western AustraliaDr Dave Smith Yale-NUS CollegeProf Kate Smith-Miles The University of MelbourneMr Daniel Snells The University of AucklandMx Matthew James Spongs The University of MelbourneDr Belinda Spratt Queensland University of TechnologyMiss Haripriya Sridharans The University of AdelaideDr Peter Stacey La Trobe UniversityProf Yury Stepanyants University of Southern QueenslandDr Danny Stevenson The University of AdelaideDr Tim Stokes University of WaikatoProf Yvonne Stokes The University of AdelaideMiss Michelle Strumilas The University of MelbourneDr Jeremy Sumner University of TasmaniaDr Nicole Sutherland The University of SydneyMr Ahnaf Tajwar Tahabubs The University of AdelaideDr Thomas Taimre University of QueenslandMr Dominic Tates The University of SydneyProf Peter Taylor The University of MelbourneProf Natalie Thamwattana The University of NewcastleDr Guo Chuan Thiang The University of AdelaideDr Anne Thomas The University of SydneyDr Bevan Thompson The University of QueenslandMiss Lauren Thorntons University of the Sunshine CoastDr Stephan Tornier The University of NewcastleDr Timothy Trudgian UNSW CanberraDr Ilknur Tulunay University of Technology, SydneyProf Mathai Varghese The University of AdelaideMr Volodymyr Vaskovychs La Trobe UniversityDr Peter Vassiliou Australian National UniversityMr Ivo De Los Santos Vekemanss Australian National UniversityDr Geetika Verma University of South AustraliaDr Mircea Voineagu University of New South WalesDr Raymond Vozzo The University of AdelaideDr Yuguang Wang University of New South WalesProf Ian Wanless Monash UniversityProf Ole Warnaar The University of QueenslandDr Yong Wei Australian National UniversityMr Dominic Weillers Australian National University

115

List of Registrants

Miss Kym Erin Wilkinss The University of AdelaideProf Geordie Williamson The University of SydneyProf George Willis The University of NewcastleDr Robert Womersley University of New South WalesMr Adam Woods The University of MelbourneMs Yuhan Wus University of WollongongDr Yaping Yang The University of MelbourneMr Yeeka Yaus The University of SydneyMr Sungha Yoons Korea UniversityMr Marley Youngs University of New South WalesDr Gufang Zhao The University of MelbourneDr Zongzheng Zhou Monash UniversityAssoc Prof Ilze Ziedins The University of AucklandAssoc Prof Paul Zinn-Justin The University of Melbourne

116

Index of Speakers

Adderton, Remy Alexander (12.1), 85

Afsar, Zahra (8.1), 74Al-shakarchi, Shaymaa Shawkat Kadhim (8.2), 74

Albion, Seamus (19.1), 106

Albrecht, Amie (14.1), 89Alizadeh, Faezeh (2.1), 56, (8.3), 74

Alpcan, Tansu (17.1), 97Ambattu Asokan, Ambily (2.2), 56

Armstrong, Becky (8.4), 74

Arroyo, Romina Melisa (6.1), 69, (9.1), 78

Bakhtawar, Ayreena (16.1), 95

Bapat, Asilata (19.2), 106

Baraglia, David (6.2), 69Batayneh, Fawwaz (7.1), 72

Beaton, Nicholas (15.1), 93Bendit, Theo (17.2), 97

Bettiol, Renato Ghini (1.1), 53, (6.3), 69

Bishop, Alex (2.3), 56Bordignon, Matteo (16.2), 95

Borovkov, Kostya (18.1), 102

Bos, Philip (16.3), 95Bradford, Elizabeth (8.5), 74

Breuer, Florian (16.4), 95

Bridges, Lachlan James (18.2), 102Brightwell, Graham (18.3), 102

Broadbridge, Philip (15.2), 93

Brook, David Leonard (8.6), 75Brothier, Arnaud (15.3), 93, (8.7), 75

Brownlowe, Nathan (8.8), 75Buciumas, Valentin (19.3), 106

Bui, Anh (11.1), 83

Bui, Thi Hoa (17.3), 97Burachik, Regina (1.2), 53

Burton, Benjamin (10.1), 80Bywaters, Timothy Peter (2.4), 56

Campbell, Alexander (4.1), 64

Chaudhuri, Anupam (15.4), 93Chen, Mike (13.1), 87

Chen, Yi-Lung (18.4), 102

Cheng, Hanz Martin (5.1), 66Cheng, Xing (11.2), 83

Choi, Jeongwhan (15.5), 93Clancy, Kieran (3.1), 60Cohen, Samuel (18.5), 102

Collevecchio, Andrea (18.6), 103

Cudmore, Peter (7.2), 72Cully-Hugill, Michaela (16.5), 95

Dao, Minh N. (17.4), 97de Silva, Raveen Daminda (8.9), 75

Dearricott, Owen (6.4), 69

Deopurkar, Anand Rajendra (16.6), 95Dick, Josef (1.3), 53

Dizon, Neil Kristofer (11.3), 83

Doan, Hong Chuong (11.4), 83Dodd, Roland (14.2), 89

Donovan, Diane (14.3), 89Dorji, Kumbu (6.5), 69

Doust, Ian (8.10), 75

Dragomir, Silvestru Sever (8.11), 75

Droniou, Jerome (5.2), 66

Duong, Xuan (11.5), 83

East, James (2.5), 56

Eastwood, Michael (6.6), 69

Eberhard, Andrew Craig (17.5), 97Ehrig, Michael (19.4), 106

Ermakov, Andrei (3.2), 60

Flood, Keegan (6.7), 69

Fok, Chi-Kwong (10.2), 80

Forrester, Peter (12.2), 85Francis-Staite, Kelli (6.8), 70

Freedman, Saul (19.5), 106

Freire, Wilhelm (17.6), 98

Gaitsgory, Vladimir (17.7), 98

Galapitage, Ajini (3.3), 60Gallo, Anthony John (13.2), 87

Garoni, Timothy (15.6), 94

Garrido, Alejandra (2.6), 57Gepner, David (2.7), 57, (4.2), 64

Ghys, Etienne (1.4), 53, (20.1), 110Gibson, Joel (19.6), 106

Giudici, Michael (2.8), 57Glasby, Stephen (2.9), 57

Glynn, David G (10.3), 80

Gobet, Thomas (19.7), 107Goh, Yoong Kuan (13.3), 87

Gonzalez-Tokman, Cecilia (7.3), 72

Guanheng, Chen (10.4), 80Guo, Hailong (5.3), 66

Guo, William (14.4), 89

Halacheva, Iva (10.5), 80, (19.8), 107

Ham, Sophie (10.6), 80

Hamza, Kais (18.7), 103Han, Fei (8.12), 76

Hartley, David (14.5), 90, (9.2), 78

Haythorpe, Michael (5.4), 66He, Jian (10.7), 81

Hegland, Markus (5.5), 67

Hekmati, Pedram (9.3), 78Henderson, Anthony (19.9), 107

Heng, Edmund Xian Chen (19.10), 107

Hodgkinson, Liam (18.8), 103Howlett, Phil (17.8), 98

Hussain, Mumtaz (16.7), 96

Jackson, Deborah (14.6), 90

James, Simon (14.7), 90

Jansen, Hermanus Marinus (18.9), 103Jensen, Iwan (15.7), 94

Joshi, Nalini (12.3), 85

Jovanoski, Zlatko (3.4), 60

Kajiwara, Kenji (12.4), 85

Kamgarpour, Masoud (19.11), 107Kandanaarachchi, Sevvandi Priyanvada (3.5), 61

Kaya, Yalcin (17.9), 98

Kennett, Carolyn (14.8), 90Kerschl, Alexander Ferdinand (19.12), 107

Khanh, Tran Vu (11.6), 83

117

Index of Speakers

King, Carlisle (2.10), 57

Kirszenblat, David (17.10), 98

Kleshnina, Maria (13.4), 87Krakowski, Krzysztof (6.9), 70

Krings, Marvin (19.13), 107

Krishnapur, Manjunath (1.5), 53Kruger, Alexander (17.11), 99

Kumar, Neeraj (2.11), 58

Kwong, Kwok-Kun (9.4), 78

Lafuente, Ramiro Augusto (6.10), 70, (9.5), 78

Le Gia, Quoc Thong (5.6), 67Leplaideur, Renaud (7.4), 72

Lewis, Angus Hamilton (18.10), 103

Li, Guoyin (17.13), 99Licata, Joan (1.6), 54

Lim, Johnny (8.13), 76

Lishak, Boris (10.8), 81Lonsdale, Heather (14.9), 90

Loxton, Ryan (17.14), 99Luczak, Malwina (1.7), 54

Ludewig, Matthias (10.9), 81, (8.14), 76

Lopez Cerda, Marco Antonio (17.12), 99

Maehara, Yuki (4.3), 64

Mak, Chi (14.10), 91Maldon, Benjamin (3.6), 61

Mampusti, Michael Arthur (8.15), 76

Mansfield, Daniel Francis (10.10), 81Marangell, Robert (7.5), 72

Marshall, Anthony Shane (6.11), 70

Marshman, Margaret (14.11), 91Maurer, Helmut (17.15), 99

Mays, Anthony (15.8), 94

McCoy, James (9.6), 79McDougall, Robert (2.12), 58

McGuinness, Mark Joseph (3.7), 61

McLean, William (5.7), 67Moka, Sarat Babu (18.11), 104

Moore, Ross (14.12), 91

Morrill, Thomas (16.8), 96Murphy, Jessica (8.16), 77

Murray, Michael (6.12), 71

Nam, Kihun (18.12), 104Naqvi, Yusra (19.14), 108

Nelson, Mark (3.8), 61Newcombe, Alex (5.8), 67

Newsam, Garry (5.9), 67Nguyen Duy, Cuong (17.16), 100

Oates, Greg (14.13), 92

Olenko, Andriy (18.13), 104Osinga, Hinke (1.8), 54

Ottazzi, Alessandro (6.13), 71

Parker, Brett (10.11), 81, (9.7), 79

Peralta, Oscar (18.14), 104

Pettersson, William Erik (17.17), 100, (3.9), 62Pickenhain, Sabine (17.18), 100

Planiden, Chayne (17.19), 100

Quispel, Reinout (12.5), 85

Rieger, Janosch (17.20), 100, (5.10), 67

Roberts, Timothy (7.6), 72Robertson, David (2.13), 58

Robertson, Marcy (4.4), 64Robins, Vanessa (10.12), 81, (3.10), 62

Romanov, Anna (19.15), 108

Rose, Danya (13.5), 87

Scheckter, Thomas (8.17), 77Schmalz, Gerd (6.14), 71

Schmalz, Jelena (14.14), 92Scrimshaw, Travis (19.16), 108

Seaton, Nicholas (8.18), 77

Sha, Min (16.9), 96Shanmugalingam, Nageswari (1.9), 54

Shen, Yibing (12.6), 85

Sherwood, Steven (1.10), 55Shi, Yang (12.7), 85

Simon, Miles (9.8), 79

Small, Michael (7.7), 73Smith, Dave (7.8), 73

Snell, Daniel (6.15), 71Spong, Matthew James (19.17), 108

Spratt, Belinda (17.21), 101

Stepanyants, Yury (12.8), 86Stevenson, Danny (4.5), 64

Stokes, Tim (2.14), 58

Stokes, Yvonne (3.11), 62Strumila, Michelle (4.6), 64

Sumner, Jeremy (13.6), 88, (2.15), 58

Sutherland, Nicole (16.10), 96

Tahabub, Ahnaf Tajwar (9.9), 79

Tate, Dominic (10.13), 82Taylor, Peter (18.15), 104

Thamwattana, Natalie (1.11), 55

Thiang, Guo Chuan (8.19), 77Thomas, Anne (10.14), 82

Thornton, Lauren (2.16), 58

Tornier, Stephan (2.17), 59Trudgian, Timothy (16.11), 96

Tulunay, Ilknur (3.12), 63

Varghese, Mathai (8.20), 77

Vaskovych, Volodymyr (18.16), 105

Vassiliou, Peter (6.16), 71Vekemans, Ivo De Los Santos (4.7), 64

Verma, Geetika (11.7), 84

Wang, Yuguang (5.11), 68

Warnaar, Ole (16.12), 96

Wei, Yong (9.10), 79Weiller, Dominic (4.8), 65

Williamson, Geordie (1.12), 55

Willis, George (2.18), 59Womersley, Robert (5.12), 68

Wood, Adam (10.15), 82

Wu, Yuhan (9.11), 79

Yau, Yeeka (2.19), 59

Young, Marley (16.13), 96

Zhou, Zongzheng (15.9), 94

Ziedins, Ilze (18.17), 105Zinn-Justin, Paul (12.9), 86

118

Conference Timetable Summary

Monday Tuesday Wednesday Thursday Friday

8:00

8:30

9:00

9:30

10:00

10:30

11:00

11:30

12:00

12:30

13:00

13:30

14:00

14:30

15:00

15:30

16:00

16:30

17:00

17:30

18:00

18:30

19:00

19:30

20:00

WIMSIGGeneral Meeting

Women inMathematical

Sciences DinnerThe Playford

Registration

Morning Tea

Lunch

Afternoon Tea

OpeningCeremony

and Awards

WelcomeReception

Plenary LectureGeordie

Williamson

Plenary LectureMalwina Luczak

ANZIAM LectureSteven Sherwood

Special sessions(2 talks)


Morning Tea

Lunch

Debate

Award Lecture

Public LectureReception

Public LectureEtienne Ghys

Plenary LectureNatalie

Thamwattana

Plenary LectureManjunathKrishnapur

Plenary LectureJoan Licata

EA Tea

Education

Afternoon

Afternoon

Tea

Specialsessions(5 talks)

Morning Tea

Lunch

Afternoon Tea

AustMS AGM(in Horace LambLecture Theatre)

Conference DinnerNational

Wine Center

Hanna NeumannLecture

Hinke Osinga

Early CareerLecture

Renato Bettiol

Plenary LectureRegina Burachik

Plenary LectureEtienne Ghys

Optimisation &RepTheo session


Morning Tea

Lunch

Afternoon Tea


Plenary LectureJosef Dick

Plenary LectureNageswari

Shanmugalingam



The opening ceremony, all plenary lectures, the public lecture and the debate take place in the BraggsLecture theatre. Teas, coffees and lunches are served in the Atrium of the Ingkarni Wardli building,where also the Welcome Reception and the Public Lecture Reception will be held.

119

Ingkarni

Wardli

Engineering

Mathematics

Engineering

North

Engineering

South

Horace

Lamb

Barr

Smith

South

Ligertwood

1

2

3

4

5

6

7

The Braggs

8

Ingkarni

Wardli

Atrium

A

Session Building RoomAlgebra 3 Horace Lamb Lecture Theatre 1022Applied and Industrial Mathematics 8 Ligertwood 316Category Theory 5 Engineering Mathematics EMG06Computational Mathematics 8 Ligertwood 314 (Flinders Room)Differential Geometry 4 Barr Smith South 2051Dynamical Systems and Ergodic Theory 8 Ligertwood 214 (Piper Alderman Room)Functional Analysis 7 Engineering South S111Geometric Analysis 5 Engineering Mathematics EMG07Geometry and Topology 4 Barr Smith South 2060Harmonic Analysis 8 Ligertwood 111Integrable Systems 8 Ligertwood 112Mathematical Biology 8 Ligertwood 216 (Sarawak Room)Mathematical Physics 6 Engineering North N132Mathematic Education 3 Horace Lamb 422Number Theory 2 Ingkarni Wardli B17Optimisation 7 Engineering South S112Probability Theory and Stochastic Processes 2 Ingkarni Wardli B18Representation Theory 4 Barr Smith South 2052Annual General Meeting 3 Horace Lamb Lecture Theatre 1022Plenaries 1 The Braggs G60Lunch, tea and social events A Ingkarni Wardli Atrium

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