topology conf
DESCRIPTION
Topology conferenceTRANSCRIPT
YoungTopologists’Meeting
EPF Lausanne8-12 July
2013
Organizers:Varvara KarpovaMarc StephanKay WerndliDimitri Zaganidis
Coorganizers:María Calvo Cervera
Martina RovelliJustin Young
with the support of
Contents
Schedule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4Lectures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Benoit Fresse (Université Lille 1) . . . . . . . . . . . . . . . . . . . . . 6Mike Mandell (Indiana University) . . . . . . . . . . . . . . . . . . . . 6
Abstracts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7Cristina Ana-Maria Anghel (Bucharest University) . . . . . . . . . . . . . . 7Ðorđe Baralić (Mathematical Institute SASA) . . . . . . . . . . . . . . . 7Andrea Cesaro (Université Lille 1) . . . . . . . . . . . . . . . . . . . . 8Man Chuen Cheng (University of British Columbia) . . . . . . . . . . . . . 9Marek Filakovský (Masaryk University Brno) . . . . . . . . . . . . . . . . 9Saul Glasman (MIT) . . . . . . . . . . . . . . . . . . . . . . . . . . 9Moritz Groth (Nijmegen) . . . . . . . . . . . . . . . . . . . . . . . . 10Robert Hank (University of Minnesota) . . . . . . . . . . . . . . . . . . 10Julienne Houck (Western Michigan University) . . . . . . . . . . . . . . . 10Magdalena Kedziorek (Sheffield) . . . . . . . . . . . . . . . . . . . . . 10Markus Land (University of Bonn), Fabian Lenhardt (Freie Universitaet Berlin) . 11Marc Lange (Hamburg) . . . . . . . . . . . . . . . . . . . . . . . . . 11Alexander Longdon (University of Manchester) . . . . . . . . . . . . . . . 11Andor Lukacs (Babes-Bolyai University) . . . . . . . . . . . . . . . . . . 12Jeroen Maes (University of Seville) . . . . . . . . . . . . . . . . . . . . 12Sam Richard Nolen (Stanford) . . . . . . . . . . . . . . . . . . . . . . 12Martin Palmer (University of Muenster) . . . . . . . . . . . . . . . . . . 12Sune Precht Reeh (University of Copenhagen) . . . . . . . . . . . . . . . 13James Schwass (Western Michigan University) . . . . . . . . . . . . . . . 13Salvador Sierra Murillo (Freie Universität Berlin) . . . . . . . . . . . . . . 13Karol Szumiło (University of Bonn) . . . . . . . . . . . . . . . . . . . . 14Rafael Torres (University of Oxford) . . . . . . . . . . . . . . . . . . . 14Nicolas Weisskopf (University of Fribourg) . . . . . . . . . . . . . . . . . 15Luke Wolcott (University of Western Ontario) . . . . . . . . . . . . . . . 15Stephanie Ziegenhagen (Universität Hamburg) . . . . . . . . . . . . . . . 15
Accommodation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16Check-in/Check-out . . . . . . . . . . . . . . . . . . . . . . . . . . 16How to go to your accommodation . . . . . . . . . . . . . . . . . . . . 16How to go to the conference from your accommodation . . . . . . . . . . . . 17Free Wifi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17Free public transport card . . . . . . . . . . . . . . . . . . . . . . . . 17Rooms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17Contact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Excursions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18Hike: Haut-de-Caux → Col de Jaman → Montreux . . . . . . . . . . . . . 18Rope Park . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19Art Gallery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Lunch places . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20Conference Dinner . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
Restaurants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22Italian food . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22Asian food . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22Vegan food . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22Swiss restaurants . . . . . . . . . . . . . . . . . . . . . . . . . . . 23Burgers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
List of Participants . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
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Schedule
Time Monday Tuesday8:15 –8:45
Registration
8:45 –9:00
Welcome
9:00 – Benoit Fresse Benoit Fresse9:45 Lecture 1 Lecture 2
10:00 – Alexander Longdon Robert Hank10:30
K
Double point self-intersection sur-faces of immersions
Massey products in A-infinity algebras
11:00 – Martin Palmer Sam Richard Nolen11:30 Homological stability for spaces of
disconnected submanifoldsDyer-Lashof Operations and String Topol-ogy
11:45 – Rafael Torres Andrea Cesaro12:15 Exotic smooth structures on non-
orientable 4-manifolds and involu-tions
Homotopy operations on simplicial alge-bras over an operad
Lunch
13:45 – Mike Mandell Mike Mandell14:35 Lecture 1 Lecture 2
14:45 – Ðorđe Baralić Stephanie Ziegenhagen15:15
K
Topology and Combinatorics of Qu-asitoric Manifolds
Additional structures on En-cohomology
15:45 – Nicolas Weisskopf Saul Glasman16:15 Positive Curvature and Topology A quasicategorical theory of E-infinity bi-
monoids
16:30 – Cristina Ana-Maria Anghel Marc Lange17:00 Twisted polynomials for knots and
3-manifolds with applications toconcordance, slicing and fibering
A Multiplicative Delooping of BimonoidalBicategories
17:30 – Football
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Time Wednesday Thursday Friday9:00 – Benoit Fresse Benoit Fresse Mike Mandell9:45 Lecture 3 Lecture 4 Lecture 4
10:00 – Moritz Groth Luke Wolcott Julienne Houck10:30
K
A (monoidally) refinedpicture of stabilization
Bousfield lattices and smash-ing localizations of local cate-gories
A Pattern in Ljusternik-Schnirelmann category
11:00 – Karol Szumiło James Schwass Marek Filakovský11:30 Cofibration categories
and quasicategoriesPhantom Maps: Results andConjectures.
Algorithmic AlgebraicTopology
11:45 – Jeroen Maes Man Chuen Cheng Andor Lukacs12:15 The sense and (ab-
stract) nonsense of tri-angulated categories
Poincare Duality for orbifoldin Morava K-theory
Dendroidal weak 2- and3-categories
Lunch
13:45 – Excursions Mike Mandell14:30 Lecture 3
14:45 - Magdalena Kedziorek15:15
K
Towards an algebraic modelof rational equivariant cohom-ology theories
15:45 – Sune Precht Reeh16:15 Burnside rings and fusion sys-
tems
16:30 – Salvador Sierra Murillo17:00 Witt-vectors and Nil-groups
17:15 – Markus Land and FabianLenhardt
17:55 The Farrell-Jones and Baum-Connes Conjectures
19:00 –19:30
Aperitif
19:30 – Conference dinner
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Lectures
Benoit Fresse (Université Lille 1)
The homotopy theory of En-operadsEn-operads are structures introduced at the origin of operad theory for the study of iterated
loop spaces (works of Boardman-Vogt and May). The study of En-operads has been completelyrenewed during the last decade, and many new applications of this notion have been discovered inthe fields of topology and algebra, mostly after the proof of the Deligne conjecture on Hochschildcochains.
The purpose of this lecture series is to give an introduction to the homotopy theory of En-operads. I will mostly focus on the case of E2-operads, and I will explain a deep connectionbetween E2-operads and the theory of Drinfeld’s associators.
Synopsis:(1) Intro: the definition and the significance of En-operads in topology and in algebra.(2) Braids, monoidal structures, and Fiedorowicz’s characterization of E2-operads. General-
ization for higher En-operads.(3) Drinfeld’s associators and Tamarkin’s proof of the formality of E2-operads. Generaliza-
tion for higher En-operads.(4) Homotopy automorphisms of E2-operads, the Grothendieck-Teichmüller group, and out-
look.Reference:The book in preparation "Homotopy of operads and Grothendieck-Teichmüller groups I"
(updated preprint to appear soon) will serve as an overall reference for this lecture series, andgives a comprehensive bibliography of the subject.
Mike Mandell (Indiana University)
Algebraic Models for Homotopy TypesThis talk series will give an introduction to what is currently known about modeling the
homotopy theory of topological spaces by algebraic structures refining cohomology.Lecture 1: Models in Homotopy TheoryQuillen invented model categories precisely to study the question of algebraic models for
homotopy theory. The language of closed model categories gives powerful tools for studyingabstract homotopy theory. This talk will review the concepts and language of closed modelcategories for use in later talks.
Lecture 2: Algebraic Models in Rational Homotopy TheoryHomotopy theory can be "localized" and studied at different primes. Rational homotopy
theory is a piece of homotopy theory that keeps only the information seen by the rationalnumbers, for example, the rational homology and the torsion-free part of the higher homotopygroups of simply connected spaces. Quillen and Sullivan proved that the rational homotopytheory of finite type simply connected spaces is modeled by commutative differential gradedalgebras.
Lecture 3: Algebraic Models in p-adic Homotopy TheoryFor a prime p, p-adic homotopy theory keeps track of p-torsion phenomena. For example,
information about a space remaining in the p-adic homotopy category includes cohomologywith coefficients in the p-adic numbers and for finite type simply connected spaces, the p-completion of their higher homotopy groups. Although p-adic homotopy theory of finite type
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simply connected spaces cannot be modeled by commutative differential graded algebras, it ismodeled by a generalization, E∞ differential graded algebras.
Lecture 4: Algebraic Models for Integral Homotopy TypesAfter fracturing a space into its rational and p-adic parts, it can be reconstituted by patching
data to its original homotopy type. However, the models described in the previous lectures do notpatch together to give a model for homotopy theory, and there is currently no known algebraicmodel for the homotopy theory of finite type simply connected spaces. Nevertheless, they do fittogether well enough to find models to distinguish different homotopy types of finite type simplyconnected spaces.
Abstracts
Cristina Ana-Maria Anghel (Bucharest University)
Twisted polynomials for knots and 3-manifolds with applications to concordance,slicing and fibering
The purpose of my talk is to present some applications of twisted Alexander polynomials.After a short introduction of Alexander-Conway and Jones polynomials, I shall present thedefinition of twisted Alexander polynomials and modules after Wada [4] and Lin [3]. The mainpart of my talk will be concerned with the applications of twisted polynomials to concordance,slicing and fibering of knots and/or 3-manifolds following Kirk-Livingston [2] and Friedl-Vidussi[1].
References
[1] S. Friedl, S. Vidussi Twisted Alexander polynomials detect fibered 3-manifolds Ann. ofMath. Vol. 173 , Issue 3, pp. 1587-1643, (2011).
[2] P. Kirk, C. Livingston Twisted Alexander invariants, Reidemeister torsion and Casson-Gordon invariants Topology Vol. 38, No. 3, pp. 635-661, (1999).
[3] X. S. Lin, Representations of Knot Groups and Twisted Alexander Polynomials Acta Math-ematica Sinica, English Series, July, (2001), Vol.17, No.3, pp. 361-380.
[4] M. Wada, Twisted Alexander polynomials for finitely presented groups Topology Vol. 33,No. 2, pp. 241-256, (1994).
Ðorđe Baralić (Mathematical Institute SASA)
Topology and Combinatorics of Quasitoric ManifoldsQuasitoric manifolds are introduced by Davis and Januszkiewicz in [5] where they described
their cohomology ring and various topological invariants. They have nice combinatorial andgeometrical properties which are exposed in monograph [4]. The orbit space of torus actionis combinatorial simple polytope and these manifolds are closely related to Polyhedral productfunctor.
Our goal is to show some interesting facts about these manifolds based on papers [1] and[2]. We described several sets D(M,N) of integers which could be realized as the mappingdegree of certain map f : M → N where M and N are 2n-dimensional quasitoric manifolds.Also we construct quasitoric manifold over cube In that could not be totally skew embedded
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in R8n−4α(n)+1, which is by famous result of Massey [9], the best possible bound that could beobtained using the theory of Stiefel-Whitney classes for complex manifolds. Using combinatorialproperties of the cohomology ring H∗(Q2n,Z2), we construct an interesting general non-trivialexample distinct then known example of complex projective spaces.
Combinatorial properties of polytope P and the characteristic matrix Λ say lot about topol-ogy and geometry of quasitoric manifolds over P . This is important class of complex manifoldswhich are topological analogue of toric varieties from algebraic geometry. Quasitoric manifoldsare common point of modern mathematical disciplines such as toric topology, algebraic geometry,topology, combinatorics and etc.
References
[1] Dj. Baralić, On Non-Zero Degree Maps between Quasitoric 4-manifolds,http://arxiv.org/abs/1301.0848, sent
[2] Dj. Baralić, Note on Skew Embeddings of Quasitoric Manifolds over Cube, in preperation
[3] Dj. Baralić, B. Prvulović, G. Stojanović, S. Vrećica and R. Živaljević. Topological Obstruc-tions to Totally Skew Embeddings. Transactions of American Mathematical Society. AMS,(2012), vol. 364 no. 4, 2213-2226.
[4] V. Buchstaber and T. Panov, Torus Actions and their applications in topology and combi-natorics, AMS University Lecture Series, volume 24, (2002).
[5] M. Davis and T. Januszkiewicz, Convex polytopes, Coxeter orbifolds and torus actions,Duke Math. J. 62 (1991), no. 2, 417451.
[6] H. Duan and S. Wang, Non-zero Degree Maps between 2n-manifolds, Acta Math. Sin. (Engl.Ser.) 20 (2004), no. 1, 1–14.
[7] H. Duan and S. Wang, The degrees of maps between manifolds, Mathematische Zeitschrift
[8] M. Ghomi, S. Tabachnikov. Totally skew embeddings of manifolds. Math. Z. (2008) 258:499–512.
[9] W.S. Massey. On the Stiefel-Whitney classes of a manifold. Amer. J. of Math., 82 (1960),92–102.
[10] P. Orlik and F. Raymond, Actions of the torus on 4-manifolds, Trans. Amer. Math. Soc.152 (1970), 531-559.
[11] Günter M. Ziegler, Lectures on Polytopes, Springer (1995)
Andrea Cesaro (Université Lille 1)
Homotopy operations on simplicial algebras over an operadIt is well known, following H. Cartan’s classic results, that the homotopy of a commutative
algebra, in positive characteristics, is endowed with a divided power algebra structure. B. Fressedemonstrated that it is possible to extend this result to any simplicial P -Algebra, with P anoperad. Here a divided power algebra structure is to be understood as ΓP -Algebra structure.In this talk I wish to introduce the definition of ΓP -Algebra and to discuss the structure of thehomotopy of a simplicial P -Algebra.
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Man Chuen Cheng (University of British Columbia)
Poincare Duality for orbifold in Morava K-theoryIt was showed by Greenlees and Sadofsky that the classifying spaces of finite groups are
self-dual with respect to Morava K-theory K(n). Their duality map was constructed using atransfer map. I will describe a generalization of their map which would induce a K(n)-versionof Poincare duality for classifying spaces of orbifolds. Some examples of K(n)-fundamental classand intersection product will be given. If time permits, I will explain the similarity of thisduality map with that of the Spanier-Whitehead duality for manifolds from the point of view ofdifferentiable stacks.
Marek Filakovský (Masaryk University Brno)
Algorithmic algebraic topologyThe problem of computing the structure of the set [X,Y ], i.e. the set of homotopy classes of
maps f : X → Y is one of the classical problems in algebraic topology and the pursuit of resultsin this field has introduced a lot of ideas. Therefore it is natural to ask under what conditionsthe structure can be computed algorithmically or decide whether in some cases there is no suchalgorithmic solution. As we are dealing with algorithms, this topic has obvious overlaps intocomputer science.
It is well known, that when the spaces X,Y are in the stable range, [X,Y ] has a structureof finitely generated Abelian group. Recently, it has been proven that there is an algorithmthat computes the presentation of this group. In the talk I will present an algorithm decidingwhether two maps f, g ∈ [X,Y ] are homotopic in the case that Y is simply–connected finitesimplicial set and X is a finite simplicial set.
References
[1] M.Čadek, J.Matoušek, M.Krčál, F. Sergeraert, L.Vokřínek, U.Wagner Computing all mapsinto a sphere, Preprint,arXiv:1105.6257, 2011. Extended abstract in Proc. ACM-SIAM Sym-posium on Discrete Algorithms(SODA 2012).
[2] M.Čadek, J.Matoušek, M.Krčál, L.Vokřínek, U.Wagner Algorithmic solvability of lifting ex-tension problem, Preprint 2013.
[3] C.Sims Computation with Finitely Presented Groups, Cambridge University Press 1994.
Saul Glasman (MIT)
A quasicategorical theory of E-infinity bimonoidsMay’s theory of ‘pairs of operads’ aff ords us entry to the well-forti fied land of spaces which
have two operad actions, one of which distributes over the other. From this springs the def-inition of an E-infinity ring space, the natural topological analog of a commutative semiring.We summon various combinatorial entities which allow us to reconstruct this coherent bicom-mutativity in the language of quasicategories. By way of application, we give a new proof thatthe K-theory of a commutative ring is an E-infinity ring spectrum, as well as a definition ofsymmetric bimonoidal quasicategory.
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Moritz Groth (Nijmegen)
A (monoidally) refined picture of stabilizationThis talk is based on joint work with David Gepner and Thomas Nikolaus. The stabilization
of presentable ∞-categories as described by Lurie is given by the pointed reflection followed bythe passage to internal spectrum objects. Abstractly, this amounts to passing from∞-categoriesfirst to pointed ∞-categories and then to stable ∞-categories.
We introduce two additional intermediate steps given by preadditive and additive ∞-cate-gories, and show that E∞-spaces and grouplike E∞-spaces are universal examples. Moreover,all ∞-categories showing up in the stabilization process admit unique closed monoidal struturescharacterized by the fact that the free functors are uniquely symmetric monoidal. If time allowswe will indicate an application to multiplicative infinite loop space machines and algebraic K-theory.
Robert Hank (University of Minnesota)
Massey products in A-infinity algebrasMassey products arise as obstruction classes to higher order operations. We frequently
encounter objects in a category equipped with a multiplication in practice. We would like toknow whether or not the multiplication is associative. The obstruction to associativity can begiven in terms of a Massey product. When dealing with multiplicative structure, one frequentlyencounters objects equipped with an “almost but not quite” associative multiplication, or moreprecisely a homotopy associative multiplication. Such objects are known as A-infinity objectsand arise in topology as loop spaces. During the talk, I will develop the relation between Masseyproducts and multiplicative structure in such a way that the generalization of a Massey productfrom a strictly associative to an A-infinity structure arises naturally.
Julienne Houck (Western Michigan University)
A Pattern in Ljusternik-Schnirelmann categoryThe Ljusternik-Schnirelmann category of a space is one less than the number of contractible
open sets with which we can cover the space. If we look at the LS categories of the skeleta of aCW complex, we find a sequence of dimensions where the LS category changes. In this talk Idiscuss whether certain "categorical sequences" (defined in the paper of this name by Nendorf,Scoville, and Strom) could be realized as the categorical sequences of rational spaces. I will firstreduce from looking at all rational spaces to only Postnikov sections of finite wedges of spheres.Time permitting, I will show a simple pattern in the rational realizability of these sequences.
Magdalena Kedziorek (Sheffield)
Towards an algebraic model of rational equivariant cohomology theoriesCohomology theories are represented by spectra. However, the category of spectra is quite
complicated. The machinery of model categories allows us to look for different (easier, algebraic)models with the same homotopy information as the category of spectra. It is well known thatrational chain complexes give an algebraic model for the rational cohomology theories. However,for G-equivariant cohomology theories, no general result of this form is known when G is acompact Lie group. In this talk I will describe some earlier work and introduce a framework forconstructing algebraic models in general. It is conjectured that the models will take the form ofsheaves of modules over a topological category of subgroups of G.
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Markus Land (University of Bonn), Fabian Lenhardt (FreieUniversitaet Berlin)
The Farrell-Jones and Baum-Connes ConjecturesWe introduce the Farrell-Jones conjectures concerning algebraic K-and L-theory of group
rings and the Baum-Connes conjecture concerning the topological K-theory of a certain com-pletion of the group ring to a C∗-algebra, which are formally very similar. The conjectures areimportant in the study of high-dimensional manifolds - the Farrell- Jones conjecture is connectedto surgery theory and the Baum-Connes conjecture to index theory. We want to mention someof these applications, for example to the Borel conjecture or the Novikov conjecture. Despitetheir formal similarities, nearly all known proofs of cases of the conjecture are very different.We will try to give the basic idea behind a common proof strategy.
Marc Lange (Hamburg)
A Multiplicative Delooping of Bimonoidal BicategoriesAt least since Robert Thomason’s paper "Symmetric Monoidal Categories model all Connec-
tive Spectra" in 1995 and the infinite loop space machines of May and Segal it has been a fruitfulendeavour to use symmetric monoidal categories as combinatorial models for phenomena in sta-ble homotopy theory. Further refinements of those machines by May and Elmendorf-Mandellallow for the study of ring spectra by bimonoidal categories. A result of Baas, Dundas, Richterand Rognes allows to interpret the two-step process of building K-theory of the spectrum as-sociated to a symmetric bimonoidal category as just one construction on the category itself.By work of Angelica Osorno this equivalence is indeed one of spectra. She used an adequatedelooping of monoidal bicategories for that effort.
In order to understand the multiplicative structure on such a spectrum I want to refine thisdelooping to a multiplicative delooping of bicategories in the spirit of Elmendorf’s and Mandell’s"Rings, Modules and Algebras in Infinite Loop Space Theory". By uniqueness results regardingK-theory and the trace map K → THH of Blumberg, Gepner and Tabuada this should yield anillumating proof to the phrase: The trace map from algebraicK-theory to topological Hochschildhomology is compatible with involutions.
In particular this result would allow to structure Christian Ausoni’s calculation of V (1)∗K(ku)with respect to the natural involution given by complex conjugation on ku = K(C), which isthe endeavour that started this work.
Alexander Longdon (University of Manchester)
Double point self-intersection surfaces of immersionsGiven a smooth, compact, closed manifold M , the bordism classes of codimension k immer-
sions into n-dimensional real space are in one-to-one correspondence with elements of the stablehomotopy group πSnMO(k). By taking an element of this group and studying its image un-der the stable Hurewicz homomorphism hS : πSnMO(k) → HnMO(k) we can recover geometricinformation about the corresponding immersion.
In particular, given a self-transverse immersion f : Mk+2 → R2k+2 the set of all doubleintersection points in the image of f is itself the image of an immersion of a smooth surface.We then ask which surfaces can arise in this way. Following joint work by Peter Eccles andMohammad Asadi-Golmankhaneh and using the method outlined above, we shall see that thisself-intersection surface can be non-orientable only for certain odd values of k. If time andenthusiasm remain we shall then look at which stably complex structures can arise on these
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surfaces if we insist that our immersion itself has a stably complex structure, which is my ownwork.
Andor Lukacs (Babes-Bolyai University)
Dendroidal weak 2- and 3-categoriesDendroidal sets are a tool that let us study operads and infinity-operads similarly how
simplicial sets allow us studying categories and infinity-categories via the nerve functor. Aconsequence of this property is that we can give a compact definition of weak n-categories withdendroidal sets. The first goal of the talk is to show that the dendroidal definition of weakn-categories agrees with the classical notions of bicategories and tricategories in degree 2 and 3.I will also motivate why dendroidal weak n-categories are better than the other notions of weakn-categories with examples and formulations of some open problems in higher category theory.
Jeroen Maes (University of Seville)
The sense and (abstract) nonsense of triangulated categoriesTriangulated categories play a central role in many branches of mathematics, such as algebra,
geometry, topology and mathematical physics. By providing examples we discuss two sides of acoin: one side being the triangulated structures, the other one model structures. As an outlookwe hint at to what extent the coin can be flipped, transfering model structures into triangulatedstructures, and how far these structures are apart from each other.
Sam Richard Nolen (Stanford)
Dyer-Lashof Operations and String TopologyDyer-Lashof operations are mod p homology operations on algebras over the little n-disks
operad. I will briefly describe how they’re constructed and how to calculate them. CraigWesterland showed that Dyer-Lashof operations appear non-trivially in the string topology ofspheres and real, complex, and quaternionic projective spaces. I will discuss prospects for similarcalculations in the string topology of other manifolds.
Martin Palmer (University of Muenster)
Homological stability for spaces of disconnected submanifoldsThis talk will be concerned with spaces of disconnected submanifolds: more precisely let M
be a connected open manifold and let Q be a closed manifold (which may be disconnected). Weare interested in the space (suitably topologised) of submanifolds of M diffeomorphic to Q, andhow the homology of this space depends on Q (for fixed M).
Since M is open, one can choose a canonical way of adding a new component P to a sub-manifold, which determines a map to the space of submanifolds of M diffeomorphic to Q q P .The question is then: is this map an isomorphism on homology up to some degree? (In fact,it’s easy to see that in general it is not surjective on H0, but this simply means that we shouldinstead look at each path-component of the space of submanifolds separately.)
When Q is zero-dimensional we are talking about classical (unordered) configuration spacesof points, for which there is a well-known homological stability result. The aim of this talk is todescribe a generalisation of this result to higher-dimensional submanifolds, in which the "rate"of stability depends on the number of components of Q which are isotopic to P .
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Sune Precht Reeh (University of Copenhagen)
Burnside rings and fusion systemsFor a finite group G, the Segal conjecture states that the 0’th stable cohomotopy group of
BG+, i.e. the homotopy classes of stable maps BG+, S0, is isomorphic to a suitable completion
A(G)∧ of the Burnside ring – which is the Grothendieck group of isomorphism classes of finiteG-sets, with disjoint union as addition, and cartesian product as multiplication. Every saturatedfusion system F over a p-group S has a classifying spectrum BF constructed by Kári Ragnarsson,and there is a version of the Segal conjecture relating BF to a subring of A(S) which we callthe Burnside ring A(F) for F . During this talk, I will give an introduction to the Burnside ringof a saturated fusion system and describe an explicit transfer map from A(S)∧ to A(F)∧. Wewill also see how we can use this map to get a better understanding of structure of A(F)∧.
James Schwass (Western Michigan University)
Phantom Maps: Results and Conjectures.The study of topological phantom maps arguably began with Brayton Gray’s thesis in 1965.
A map X → Y of CW complexes is a phantom map if for any finite dimensional CW complexW the composition W → X → Y is trivial. Chuck McGibbon’s article "Phantom Maps" in theHandbook of Algebraic Topology is a wonderful survey of the basic theory. We write Ph(X,Y )for the set of phantom maps from X to Y . Since the constant map is phantom, we can be surephantom maps exist. Of more interest are essential phantom maps, i.e. phantom maps that arenot nullhomotopic. Since the property of being a phantom map is, in some sense, the propertyof being "nearly" trivial, we arrive at a natural question: can we quantify how nearly trivial anessential phantom map is? This question led to the development of the Gray index of a phantommap. Using the notion of Gray index, we construct a filtration on Ph(X,Y ) following Le MinhHa and Jeff Strom. Time permitting we will turn our attention to a new homotopy invariantderived from the Gray index, and state our preliminary findings for this invariant.
Salvador Sierra Murillo (Freie Universität Berlin)
Witt-vectors and Nil-groupsLet R be a ring with 1, the Nil-groups of R are given by
NKn(R) = Kerε∗ : Kn(R(t))→ Kn(R)
where ε∗ is the map induced in K-theory by the agumentation map ε : R(t) → R sending t tozero. These groups appear in the fundamental theorem of algebraic K-theory as direct summandsof the K-theory of its (Lauerent) polynomial ring. It is well-known that NKn(R) = 0 for everyregular ring and that NKn(R) is either trivial or infinitely generated (as abelian group). Thisfact make them difficult to compute.
We study the case R = Z[G] for a finite group G. For a geometric taste think of G asthe fundamental group of space. A general strategy to study Nil-groups is to use the so-called“Verschiebung” and “Frobenius” operators. Moreover, the Nil-groups are modules over theVerschiebung and Frobenius algebra Z[N× N].
Once we assume that NKn(R) is not zero (thus infinitely generated abelian group) then wewonder whether Nil-groups are finitely generated as Z[N×N]-modules. A general answer is notknown yet and we give two examples of such computations.
We finish with a more combinatorial description of the Z[N×N]-module structure in terms ofthe completed Burnside ring. For this we introduce the concept of Witt-vector ring of the integers
14
W (Z) and use an isomorphism due to Dress and Siebeneicher between W (Z) and the completedBurnside ring of the infinite cyclic group Ω(C). Verschibung and Frobenius operators becomethen induction and restriction respectively, those are well-known in representation theory.
References
[1] G. Almkvist, “The Grothendieck ring of the category of endomorphisms", J. Algebra 28, pp.375-388, (1974)
[2] H. Bass, “Algebraic K-theory", W. A. Benjamin, Inc., New York-Amsterdam, (1968)
[3] F. Connolly; M. da Silva, “The groups N rK0(Zπ) are finitely generated Z[Nr]-modules if πis a finite group", K-theory 9, no. 1, pp. 1-11, (1995)
[4] A. Dress; C. Siebeneicher, “The Burnside Ring of Profinite Groups and the Witt VectorConstruction", Advances in Math. 70, pp. 87-132, (1988)
[5] T. Farrell, “The nonfiniteness of Nil", Proc. Amer. Math. Soc. 65, no. 2, pp. 215-216, (1977)
[6] D. Grayson, “The K-theory of endomorphisms", J. Algebra 48, pp. 439-446, (1977)
[7] C. Weibel, “Mayer-Vietoris sequences and module structures on NK", Algebraic K-theory,Evanston 1980, pp 466-493, (Lecture Notes in Math., 854), (1980)
Karol Szumiło (University of Bonn)
Cofibration categories and quasicategoriesApproaches to abstract homotopy theory fall into roughly two types: classical and higher
categorical. Classical models of homotopy theories are some structured categories equippedwith weak equivalences, for example model categories or cofibration categories in the sense ofAnderson, Baues, Brown and others. From the perspective of higher category theory homotopytheories are the same as (∞, 1)-categories and those have plenty of models, including quasicat-egories, complete Segal spaces and Segal categories.
The higher categorical approach sheds new light on homotopy theory, namely, it allows usto consider the homotopy theory of homotopy theories. Thus we can use homotopy theoreticmethods to compare various notions of homotopy theory. Most of the known notions of (∞, 1)-categories are equivalent to each other by explicit constructions and there is also a generalapproach to such comparisons due to Barwick, Schommer-Pries and Toën.
This raises a question: are the classical approaches equivalent to the higher categorical ones?I will provide a positive answer by constructing the homotopy theory of cofibration categories andexplaining how it is equivalent to the homotopy theory of (finitely) cocomplete quasicategories.
Rafael Torres (University of Oxford)
Exotic smooth structures on non-orientable 4-manifolds and involutionsWe describe how to construct inequivalent smooth structures for every closed non-orientable
4-manifold with fundamental group of order two that admits a Pin+-structure. A study of thesmooth structure on the universal cover of the manifolds constructed yield examples of exoticinvolutions. These results serve as a good excuse to review and exemplify the process of unveilingexotic smooth structures
15
Nicolas Weisskopf (University of Fribourg)
Positive Curvature and TopologyWhich manifolds are positively curved? So far, only few objects are known to admit a
metric of positive sectional curvature. However, these examples have a rich but surprisinglysimple topological structure. In this talk we will study several topological quantities, such asthe cohomology ring and the elliptic genus, in the presence of positive curvature.
Luke Wolcott (University of Western Ontario)
Bousfield lattices and smashing localizations of local categoriesGiven an object X in a well generated tensor triangulated category C (such as the stable
homotopy category, or its localizations), the Bousfield class of X is the collection of objectsthat tensor with X to zero. The set of Bousfield classes, ordered by reverse inclusion, forms alattice called the Bousfield lattice. The structure of this lattice gives insight into localizations,nilpotents, and subcategories of C. We will describe quotient functors that allow us to relatequotients of Bousfield lattices to Bousfield lattices of quotient categories. Specifically, we willdiscuss the Bousfield lattice of the E(n)-local, K(n)-local, and harmonic categories, and latticemorphisms between them. We will also discuss the telescope conjecture and generalized smashingconjecture on these local categories, and the relevance of Bousfield lattices to these questions.
Stephanie Ziegenhagen (Universität Hamburg)
Additional structures on En-cohomologyDifferential graded modules endowed with the structure of an En-algebra are algebraic ana-
logues of n-fold loop spaces. Since these algebras are defined as algebras over a certain operad,there is an associated notion of (co)homology of En-algebras. Recent efforts to understand En-homology better include a description of En-homology with trivial coefficients via an iteratedbar complex by Benoit Fresse. Based on this result Muriel Livernet and Birgit Richter give aninterpretation in terms of functor homology for commutative algebras, which Benoit Fresse thengeneralized to the case of arbitrary En -algebras. I will show how one can describe En-homologyof commutative algebras with a wider class of coefficients as functor homology. I will also discusshow the previous description allows us to define operations on the chain complex calculatingEn-cohomology.
16
Accommodation
Check-in/Check-out
Lausanne Guest House: Check in is between 15:00 and 22:00. If you can’t be there before22:00, then the night watchman will welcome you (until 2:30 am). Check out is before 11:00am.
Youth Hostel: The reception is open 24/24. Check out is before 11:00am.
How to go to your accommodation
Lausanne Guest House: From the train station (5 min walking), go down “avenue Fraisse”and,immediately after the tunnel (before the movie theater “Moderne”), take the first on yourright, then again the first on your right.
Youth Hostel (Jeunotel): You will need to buy a public transport ticket called “Grand Lau-sanne” which covers the zones 11 and 12. From the train station, take the subway (M2) towards“Ouchy” until subway station "Délices". Then take bus number 25 towards “Bourdonnette” untilthe bus stop “Bois de Vaux”.
17
The youth hostel is at 2min walking. Cross the road in direction of the “Relais de Vidy” andgo down on the “chemin du bois de Vaud”. The youth hostel is on your right before the bridge.Please note that the last bus leaves at 23:55 from “Délices” on Sunday.
How to go to the conference from your accommodation
Lausanne Guest House (∼ 25min) Go back to the train station. Take the subway (M2)towards “Croisettes” and go down at the station “Lausanne Flon”. Take the metro (M1) towards“Renens-gare”. Go down at the station EPFL. There will be arrows guiding you to the room ofthe conference (room CM3).
Youth Hostel (∼ 25min) Go back to the bus stop and take bus number 25. Go down at“Bourdonnette” and take the metro (M1) towards “Renens-gare”. Go down at the station EPFL.There will be arrows guiding you to the room of the conference (room CM3).
Free Wifi
Both accommodation provide free wifi.Lausanne Guest House wifi: name: lghlobby , password: mercure2103.
Free public transport card
Both accommodation provide free public transport cards. Please ask them at the reception.
Rooms
As previously announced, rooms will be shared.
Lausanne Guest House Here is the repartition in rooms:Room 1: Markus Land, Körschgen Alexander, Ostermayr Dominik, Szumilo Karol.Room 2: Patchkoria Irakli, Wimmer Christian, Khan Adeel, Sierra Murillo Salvador.Room 3: Yalin Sinan, Cesaro Andrea, Molinier Rémi, Ducoulombier Julien.Room 4: Nariman Sam, Hank Robert, Glasman Saul, Liu Bei.Room 5: Longdon Alexander, Palmer Martin, Ben El Krafi Badr, Baralic Djordje.
18
Youth Hostel There will be lists at the reception. When you come, you can decide in whichroom you go. There will be rooms reserved to women. Those of you who asked to be in thesame room will already be in the same room.
Contact
If you have any other question or problem during your stay, please send me an email [email protected].
19
Excursions
Hike: Haut-de-Caux → Col de Jaman → Montreux
Hiking time: 5 hours
Elevation gain: 360 m, Elevation loss: 1000 m
Approximate cost: 30 Fr. for the train ticket
To bring: Water (1.5 liters), lunch packet, sunscreen, rain jacket, shoes you are used to hikingwith
Difficulty: The hike is not technically difficult. Most of the hike is through meadows or theforest. The forest trail may be damp and thus a bit slippery at a few places. The physicaldifficulty is medium because of the change in elevation.
We will take a train to Montreux and then change to the Swiss Golden Pass Line. Gettingoff at Haut-de-Caux, we start our hike with a great view of the lake and the mountains. Thetrail through the alpine meadows leads to the Col de Jaman. Passing some cows, we will enterthe forest to hike down to the Gorge du Chauderon. This wild and natural landscape leads usback to Montreux.
You may spend the evening at the Montreux Jazz festival, enjoying some of the free concerts.
20
Rope Park
If you prefer a physically challenging activity but don’t want to go hiking, we will visit therope park in Aigle (30min by train + 20min walk). In the forest there, eight rope parcours, ofvarying difficulty, are waiting for us, on which you can cross the forest up to 15m above ground(of course always safely attached to a rope). On the way back, the train also stops in Montreux,where the well-known Jazz festival is taking place, which you might like to visit.
Unfortunately, the rope park is more on the pricey side, costing 35 Fr. per person plus thetrain ride (circa 30 Fr. round trip, depending on the group’s size). The cost of the harness andthe carabiner is included but you are required to bring stable footwear (sports shoes will do).
Art Gallery
Those who love art can join us to visit the Collection de l’Art Brut, offering a uniquecollection of international renown, committed to discovering, researching and preserving artisticcreations outside of mainstream practices.
The entrance fee is 10 Fr. (5 Fr. if you have a student card). If we are a group of at least6 people, it will cost only 5 Fr. per person. The gallery is open from 11:00 until 18:00 and islocated at Avenue des Bergières 11, Lausanne. To get there, you can take public buses n2, n3or n21 and get off at the stop “Beaulieu-Jomini”.
21
Lunch placesThere are many options for having lunch on campus as listed on the map. You can check themenus online at http://restauration.epfl.ch/.
QIF
QIG
QIJ QIK
QIH
QII
QIE
C
B A
C B A
H G
A
B
C
F G H J
A B C
G F
C B A
H
Forum R o l e x
RLC
A C D
J K LH
Diagonale
PPB
Rte de la Sorge
Rte de la Sorge
Av.
F.-
A. F
orel
eiovaS e
d eéllA
Centre de conférenceouverture 2013
Chantier
ouverture 2013Chantier
Chantier ouverture 2014
Pl. A. Turing
.
Plus d’informationssur votre mobile:http://m.epfl.ch CM 0216
Colladon
Av. Piccard
Av. Piccard
BP & PSEC
Diagonale
RLC F1 321
SV 1604
MXF 312
SG 1131
CE 2428
CM 2420
ELA 010
INM 163
CO 160
CM 2442
SG 0166
CM 2425
CM 2435
SV 1511
BC 440
RLC F1 324
QIJ 0116
CE 1711
RLC G1 350
StarlingHotel
EpicerieLe Négoce
Hong Thai Rung
Maharaja
Obeirut Express
Fleur de Pains
Kebab & Pizza
Roulottes10:0013:30
08:0009:30
Cafétérias
Cafétéria Paul Klee
Cyber Café SV
Cafétéria MX
Cafétéria Giacometti
Cafétéria L’Arcadie
Cafétéria Satellite
Cafétéria ELA
Cafétéria INM
L’Esplanade
L’Atlantide
Le Corbusier
Le Vinci
Le Parmentier
Ornithorynque
Cafétéria BC
Le Hodler
Self-services
Le Puur Innovation
RestaurantsLe Copernic
La Table de Vallotton
Bistro 31
RESTAURATION
22
Conference DinnerThe Conference Dinner will take place at Le Châlet Suisse on Thursday, July 11, at 19:30. Itis an authentic Swiss restaurant located in the Sauvabelin woods, above Lausanne, and not farfrom the city center. The address of the restaurant is Route du Signal 40, Lausanne.
Before the dinner, starting from 19:00 there will be an Aperitif on a terrace near the restau-rant, with a picturesque view on Lausanne and Lake Geneva.
There are two ways to get to the restaurant: you can either walk from the metro stationFlon or Riponne-Maurice Béjart or use public transport.
To get there by public transport, you can take Bus n16 (direction: Grand-Vennes) at “Flon”and take off at “Signal” stop. The map below shows you how to get from the bus stop “Signal”to the terrace, where the Aperitif will be held.
If you prefer to walk, go to the Place du Tunnel. Walk up the stairs west of the tunnel. Crossthe road to take the Chemin du Petit Château. When you reach its end, turn right. Follow thewalking trail to the Museum Fondation de l’Hermitage and then continue walking uphill. After500m you reach the terrace from below.
23
RestaurantsThere are many places, where you can go for dinner. Tap water is usually free, ask for “unecarafe d’eau”. Here some options:
Italian food
• Le Relais de Vidy, close to the Jeunotel, restaurant pizzeria.Chemin du Bois-de-Vaux 20, 1007 Lausanne.+41 21 312 40 87
• Boccalino, in Ouchy, restaurant pizzeria... on Monday: Each Pizza for “only” 14 Fr.!Avenue d’Ouchy 76, 1006 Lausanne.+41 21 616 35 39
• le Milan, close to the Lausanne Guesthouse, restaurant pizzeria.Boulevard de Grancy 54, 1006 Lausanne.+41 21 616 53 43
Asian food
• Chez Xu, close to the train station, Chinese restaurant.Rue du Petit-Chêne 27, 1003 Lausanne.+41 21 320 72 68.
• Chez Xu, at Riponne, Chinese restaurant.Rue du tunnel 10, 1005 Lausanne.+41 21 312 40 87
• le Dragon, next to the train station in Renens, Chinese and Thai restaurant.Avenue de la Gare 2, 1022 Chavannes-prés-Renens.+41 21 634 02 73.
Vegan food
• Chez Sait, a Middle Eastern fast food place, near Riponne two stops on the métro northof the train station. They have falafel, but you must ask for "pas de sauce blanche". Thereare many places like this in Lausanne, in fact there is one right across the street from thisone. Just look for "Kebab" or even "Kebap".Place du Tunnel 14, 1005 Lausanne+41 21 311 86 22.
• Brasserie Artisanale du Château, a brewery with homemade beer, also near Riponne. Theyhave pizza which you can ask for "sans fromage" (without cheese), this trick will work atany restaurant with pizza, as there is usually a vegetarian pizza. Just make sure it doesn’thave "thon" (tuna) on it, this is sometimes considered "végétarien".Place du Tunnel 1, 1005 Lausanne+41 21 312 60 11.
• Holy Cow !, a fast food burger place, near Flon one stop on the métro north of the trainstation. They have multiple veggie burgers, to be vegan some must be ordered "sans
24
fromage", and also "sans mayonaise" (they all come standard with mayo).Rue des Terreaux 10, 1003 Lausanne+41 21 323 11 66.
• Lalibela, an Ethiopian restaurant, very good, there is another one across and down thestreet owned by the same people, both near Riponne.Rue du Valentin 23, 1004 Lausanne+41 21 312 00 05.
Swiss restaurants
• Café de Grancy, south of the train station, café restaurant.Avenue du Rond-Point 1, 1006 Lausanne.+41 21 616-86 -66.
• Café des Bouchers, in Malley, café restaurant.Avenue du Chablais 21, 1008 Prilly.+41 21 624 08 08.
• la Chandeleur, close to the cathedral, crêperie.Rue Mercerie 9, 1003 Lausanne.+41 21 312 84 19.
Burgers
• le Brasseur, close to Flon, brasserie.Rue Centrale 4, 1003 Lausanne.+41 21 351 14 24.
• Holy cow, close to Bel-Air, gourmet burger.Rue des Terreaux 10, 1003 Lausanne.+41 21 329 03 23
• Great Escape, walk up the stairs at Riponne, bar restaurant.Rue Madeleine 18, 1003 Lausanne.+41 21 312 31 94
25
List of ParticipantsAdrom
Pouy
aUniversity
ofGlasgow
p.ad
Agy
ingi
Collin
sAmbu
roUniversity
ofCap
eTo
wn
agying
i.collin
sambu
ro@uc
t.ac.za
Ang
hel
Cris
tinaAna
Maria
Bucha
rest
University
simple_
words91
@yaho
o.com
Baralic
Djordje
Mathe
matical
Institu
teSA
SAdjba
u.ac.rs
Bayeh
Marzieh
University
ofRegina
bayeh2
Ben
ElKrafi
Bad
rFa
culté
desscienc
esAïn
Cho
ckCasab
lanc
abe
nelkrafi@
gmail.c
omBergsaker
Håkon
University
ofBergen
hakonsb@
math.uio.no
Calvo
María
Universidad
deGrana
damariacc@ug
r.es
Carlso
nMag
nus
Stockh
olm
University
mag
Caviglia
Giovann
iRad
boud
University
Nijm
egen
Cesaro
And
rea
Université
Lille
1an
drea.cesaro@
ed.univ-lille1.fr
Che
ngMan
Chu
enUniversity
ofBrit
ishColum
bia
mcche
c.ca
Colum
bus
Tobias
Karlsr
uher
Institu
tfürTe
chno
logie
tobias.colum
bus@
kit.e
duDan
eshp
ajou
hHam
idReza
Institu
teforResearchin
Fund
amentalS
cien
ces(IPM
)hr.dan
eshp
ajou
h@gm
ail.c
omDeh
ling
Malte
University
ofGoettingen
mde
hling@
gmail.c
omDon
ovan
Micha
elMassachusetts
Institu
teof
Techno
logy
Mdo
uDossena
Giacomo
SISS
Ado
ssen
a@sis
sa.it
Duc
oulombier
Julie
nUniversité
Paris
13/laga
ducoulom
iv-paris1
3.fr
Dvirnas
Albertas
Kau
nasUniversity
ofTe
chno
logy
retarded
shrim
p@gm
ail.c
omEg
asSa
ntan
der
Dan
iela
University
ofCop
enha
gen
daniela@
math.ku
.dk
Egger
Philip
Northwestern
University
philip.egger@
math.no
rthw
estern.edu
Fernan
dez-Va
lenc
iaRam
ses
Swan
seaUniversity
rojotiz
on@gm
ail.c
omFilakovsky
Marek
Masaryk
University
Brno
m.filakovsky
@sezn
am.cz
Foley
John
University
ofCop
enha
gen
foley@
math.ku
.dk
Fresse
Ben
oît
Université
Lille
1Ben
oit.F
resse@
math.un
iv-lille
1.fr
Ghe
orgh
eBog
dan
Wayne
StateUniversity
gheorghe
bg@way
ne.edu
Glasm
anSa
ulMIT
sglasm
uGom
ezLo
pez
Mau
ricio
University
ofCop
enha
gen
xqf159
@alum
ni.ku.dk
Grey
Matthias
University
ofCop
enha
gen
m.grey@
math.ku
.dk
Han
kRob
ert
University
ofMinne
sota
hank
x003
@um
n.ed
uHau
sman
nMarku
sUniversity
ofBon
nmarku
shm@un
i-bon
n.de
Høg
enha
ven
Amalie
University
ofCop
enha
gen
bvc174
@alum
ni.ku.dk
Hou
ckJu
lienn
eWestern
Michiga
nUniversity
julie.hou
u
26
Istrati
Nicolina
University
ofBucha
rest
nicolin
a_i@
yaho
o.com
Joachimi
Ruth
University
ofWup
pertal
joachimi@
uni-w
uppe
rtal.de
Joha
nsen
Rasmus
University
ofCop
enha
gen
crg7
22@alum
ni.ku.dk
Karpo
vaVa
rvara
EPFL
varvara.ka
rpova@
epfl.ch
Ked
ziorek
Mag
dalena
University
ofSh
effield
pmp1
0mk@
sheffi
eld.ac.uk
Kha
nAde
elFreieUniversitä
tBerlin
kade
el@gm
ail.c
omKiw
iLe
vUniversity
ofFribou
rglev.kiwi@
unifr.ch
Kjæ
rJens
Jakob
University
ofCop
enha
gen
m08
.dk
Klamt
Ang
ela
University
ofCop
enha
gen
.dk
Körschg
enAlexa
nder
University
ofBon
nalexan
der@
koerschg
en.nam
eKrasontov
itsch
Valentin
University
ofBergen
v.krason
tov@
gmail.c
omLa
ndMarku
sUniversity
ofBon
nland
@math.un
i-bon
n.de
Lang
eMarc
Ham
burg
marc@
lang
e-iz.de
Lenh
ardt
Fabian
FreieUniversita
etBerlin
lenh
.de
LiDu
University
ofGoettingen
lidu@
uni-m
ath.gw
dg.de
Liu
Bei
University
ofGoettingen
berenliu@gm
ail.c
omLo
ngdo
nAlexa
nder
University
ofMan
chester
alexan
der.lon
gdon
@po
stgrad
.man
chester.a
c.uk
Luka
csAnd
orBab
es-B
olyaiU
niversity
luka
cs.and
or@gm
ail.c
omMaes
Jeroen
University
ofSe
ville
jmaes@
us.es
Man
dell
Micha
elIndian
aUniversity
mman
dell@
indian
a.ed
uMcG
illCallan
University
ofSh
effield
calla
n.mcgill@gm
ail.c
omMercier
Valentin
EPFL
valen.mercier@gm
ail.com
Moi
Kris
tianJo
nsson
University
ofCop
enha
gen
.dk
Molinier
Rém
iUniversité
Paris
13molinier@
math.un
iv-paris1
3.fr
Mosley
John
University
ofKentucky
john
.mosley@
uky.ed
uNaa
rman
nSimon
Georg-A
ugust-Universitä
tGöttin
gen
s.naa
rman
n@gm
x.de
Narim
anSa
mStan
ford
University
narim
ford.edu
Nolen
Sam
Stan
ford
University
samno
len@
stan
ford.edu
Ostermayr
Dom
inik
University
ofBon
ndo
mi_
osterm
ayr@
web
.de
Otim
anAlexa
ndra-Iulia
University
ofBucha
rest
alexan
dra_
otim
an@yaho
o.com
Palm
erMartin
University
ofMue
nster
mpa
lm_01
@un
i-mue
nster.d
ePa
tchk
oria
Irak
liUniversity
ofBon
nira
kli.p
atchkoria
@gm
ail.c
om
27
Precht
Reeh
Sune
University
ofCop
enha
gen
spr@
math.ku
.dk
Rovelli
Martin
aEP
FLmartin
a.rovelli@ep
fl.ch
Russhard
And
rew
Southa
mpton
University
andrew
.russha
rd@gm
ail.c
omSche
lling
Arkad
iUniversity
ofFreibu
rgarka
di.sc
helling
@gm
ail.c
omSchw
ass
James
Western
Michiga
nUniversity
james.p.sc
hwass@
wmich.ed
uSierra
Murillo
Salvad
orFreieUniversitä
tBerlin
sierra.murillo@
gmail.c
omSo
lberg
Mirjam
University
ofBergen
mirjam
.solberg@
math.uib.no
Step
han
Marc
EPFL
marc.step
han@
epfl.ch
Szum
iloKarol
University
ofBon
nszum
i-bon
n.de
Torres
Rafael
University
ofOxford
Weisskopf
Nicolas
University
ofFribou
rgnicolas.w
eissko
pf@un
ifr.ch
Wen
zel
Ansga
rUniversity
ofSu
ssex
a.wen
zel@
sussex.ac.uk
Wernd
liKay
EPFL
kay.wernd
li@ep
fl.ch
Wim
mer
Christ
ian
University
ofBon
ns6chwim
m@un
i-bon
n.de
Wolcott
Luke
University
ofWestern
Ontario
luke.wolcott@gm
ail.c
omYa
linSina
nUniversité
Lille
1sin
iv-lille
1.fr
Youn
gJu
stin
EPFL
justin.you
ng@ep
fl.ch
Zaga
nidis
Dim
itri
EPFL
dimitr
i.zag
anidis@
epfl.ch
Ziegen
hagen
Step
hanie
Universitä
tHam
burg
step
hanie.ziegen
hagen@
math.un
i-ham
burg.de
