Contents

1 Welcome 1

2 Summer School 22.1 Lectures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22.2 Schedule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

3 Conference 43.1 Talks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43.2 Schedule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53.3 Abstracts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

4 Practical Information 114.1 Public transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114.2 Hotels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114.3 Summer School and Conference . . . . . . . . . . . . . . . . . . . . . . . . . . 114.4 Food and Drink . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124.5 Internet Access . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

5 Social Program 13

6 Heidelberg Sights - Top 10 14

7 Participants 15

8 Notes 17

Map - Campus Im Neuenheimer Feld (INF) 18

1 Welcome

Dear Participant,

We welcome you to the summer school and conference on ”Computations with ModularForms 2011”.

The main focus of the conference is the development and application of algorithms inthe field of modular and automorphic forms. Prior to the conference there is a summerschool in Heidelberg from Aug 29 to Sep 2. It covers several current topics of the theory andcomputation of modular forms. The summer school is aimed at young researchers and PhDstudents working or interested in this area.

This booklet contains schedules and abstracts of the talks. Moreover, you will find furtherpractical information on Heidelberg, the offered social program and a map of the campus ImNeuenheimer Feld. At the end of this booklet you will find a list of all the participants of theseevents. There are two further maps with informations on sights and connections included inyour welcome bag.

We hope you will enjoy your time at the University of Heidelberg!

The organizersGebhard Bockle, John Voight and Gabor Wiese

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2 Summer School

2.1 Lecture series

Henri Darmon - p-adic Rankin L-functions: a computational perspective

In this series, I will describe the construction of p-adic Rankin L-functions and raise thequestion of how to compute them efficiently in polynomial time.

Paul Gunnells - Arithmetic groups, automorphic forms, and Hecke operators

Arithmetic groups are discrete subgroups of Lie groups; for basic examples one should thinkof the modular group SL(2,Z), the Siegel modular group Sp(2n,Z), and their congruence sub-groups. The cohomology of such groups provides a concrete realization of certain automorphicforms, in particular automorphic forms that are conjectured to have a close relationship witharithmetic geometry. For instance, by results of Eichler-Shimura the cohomology of congru-ence subgroups of the modular group gives a way to explicitly compute with holomorphicmodular forms.

In this course we will explore this connection between topology and number theory, withthe goal of presenting tools one can use to compute with these objects. We will review thesituation for SL(2,Z) and then will discuss how one computes with other groups, especiallySL(n,Z) and GL(n) over number fields; the latter family includes Hilbert modular forms.Special emphasis will be placed on how one can compute the action of the Hecke operators onthe cohomology corresponding to cuspidal automorphic forms.

Topics for the lectures include the following: cohomology of arithmetic groups and connec-tions with representation theory and automorphic forms, modular symbols, explicit polyhedralreduction theory, Hecke operators, connections to Galois representations.

Background reading: http//:www1.iwr.uni-heidelberg.de/conferences/modularforms11/welcome/backgroundgunnels/.

David Loeffler - Automorphic forms for definite unitary groups

I will describe an approach to computing automorphic forms for a certain class of reductivegroups where the theory can be made purely algebraic. The most prominent examples of suchgroups are definite unitary groups (in any number of variables). I will explain the construction(due to Gross) of algebraic automorphic forms for such groups, and how this leads naturally toan algorithm for calculating these spaces using lattice enumeration techniques. I will illustratethis with some examples of computational results for unitary groups in 3 and 4 variables, anddescribe how the results can be interpreted in terms of Galois representations.

Robert Pollack - Overconvergent modular symbols

The theory of modular symbols, which dates back to the 70s, allows one to algebraicallycompute special values of L-series of modular forms. In the 90s, Glenn Stevens introduced thenotion of overconvergent modular symbols which is a p-adic extension of the classical theory.

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In the end, overconvergent modular symbols encode p-adic congruences between special valuesof L-series, and in particular, are intimately related to p-adic L-functions.

This course will give a down-to-earth introduction to the theory of overconvergent modularsymbols. This theory has the great feature of being extremely concrete, and as a result,extremely computable. We will explain concrete methods to compute overconvergent symbolsin practice, and as an application, one obtains algorithms to compute p-adic L-functions ofmodular forms.

Notes of an Arizona Winter School by the lecturer: http://swc.math.arizona.edu/aws/

11/2011PollackStevensNotes.pdf.

2.2 Schedule

Monday Tuesday Wednesday Thursday Friday8:00 am

8:30 am

9:00 am

9:30 am

10:00 am

10:30 am

11:00 am

11:30 am

12:00 am

12:30 am

1:00 pm

1:30 pm

2:00 pm

2:30 pm

3:00 pm

3:30 pm

4:00 pm

4:30 pm

5:00 pm

Registration & Coffee

9:20-9:50

Welcome

David Loeffler10:00-11:00

Coffee break

Paul Gunnells11:30-12:30

Lunch12:30-14:00

Robert Pollack2:00-3:00

Independentstudy groups3:00-5:00

HS 3/4

David Loeffler10:00-11:00

Coffee break

Paul Gunnells11:30-12:30

Lunch12:30-2:00

Robert Pollack2:00-3:00

Independentstudy groups3:00-5:00

HS 3/4

David Loeffler10:00-11:00

Coffee break

Paul Gunnells11:30-12:30

Lunch12:30-2:00

Robert Pollack2:00-3:00

Excursion3:00-:600

David Loeffler8:50-9:50

Robert Pollack10:00-11:00

Coffee break

Paul Gunnells11:30-12:30

Lunch12:30-2:00

Henri Darmon2:00-3:00

Independentstudy groups3:00-5:00

HS 3/4

David Loeffler8:50-9:50

Robert Pollack10:00-11:00

Coffee break

Paul Gunnells11:30-12:30

Lunch12:30-2:00

Henri Darmon2:00-3:00

Free afternoon

Location: Campus Im Neuenheimer Feld, building Mathematisches Institut (INF 288). Talksand opening will be in the lecture hall Horsaal 2 (HS 2); coffee and welcome in the foyer ofthe lecture hall.

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3 Conference

3.1 Talks

Monday, September 5

John Cremona Modular symbols over number fieldsLassina Dembele Explicit base change and congruences of Hilbert modular formsLoıc Merel Modular forms modulo 2 and modular curves over the real numbersXevi Guitart Rational points on elliptic curves over almost totally complex

quadratic extensionsNicolas Billerey Explicit Large Image Theorem for Galois Representations

attached to Modular FormsSara Arias-de-Reyna On a conjecture of Geyer and Jarden about abelian varieties over

finitely generated fieldsKathrin Maurischat On Poincare series of low weight for symplectic groups

Tuesday, September 6

Alan Lauder Computations with classical and p-adic modular formsXavier Caruso An algorithm to compute lattices in semi-stable representationsPeter Bruin Computing in Jacobians of modular curves over finite fieldsJohan Bosman Implementation presentation: computing with Galois

representations of modular formsSteve Donnelly Hilbert modular forms in Magma and tables of modular elliptic

curvesAurel Page Algorithms for arithmetic Kleinian groupsRalf Butenuth On computing quaternion quotient treesAriel Martın Pacetti Hecke-Sturm bound for hilbert modular surfacesDan Yasaki Computation of certain modular forms using Voronoi Polyhedra

(Software)

Wednesday, September 7

David Loeffler Unitary groups and even Galois representationsMatthew Greenberg Kneser’s p-neighbour construction and Hecke operators for

definite orthogonal and unitary groupsTommaso Centeleghe Computing the number of certain Galois representations mod pMax Flander Bases of Modular FormsGeorge Schaeffer The Hecke stability method

Thursday, September 8

Jan Hendrik Bruinier Coefficients of harmonic Maass formsDan Yasaki Computation of certain modular forms using Voronoi PolyhedraNils-Peter Skoruppa Computing modular forms of half integral weightCecile Armana On Manin’s presentation for modular symbols over function fieldsNils-Peter Skoruppa Computing modular forms of half integral weight (Software)

Location: the lecture hall Horsaal 2 of the building Kirchhoff-Institut fur Physik (INF 227).

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3.2 Schedule

Monday Tuesday Wednesday Thursday8:00 am

8:30 am

9:00 am

9:30 am

10:00 am

10:30 am

11:00 am

11:30 am

12:00 am

12:30 am

1:00 pm

1:30 pm

2:00 pm

2:30 pm

3:00 pm

3:30 pm

4:00 pm

4:30 pm

5:00 pm

5:30 pm

6:00 pm

Registration & Coffee8:20-8:50Welcome

John Cremona9:00-9:50

Lassina Dembele10:00-10:50

Coffee break10:50-11:30

Loıc Merel11:30-12:20

Lunch12:20-3:00

Xevi Guitart3:00-3:25

Nicolas Billerey3:35-4:00

Coffee break4:00-4:30

Sara Arias-de-Reyna4:30-4:55

Kathrin Maurischat5:05-5:30

Alan Lauder9:00-9:50

Xavier Caruso10:00-10:50

Coffee break10:50-11:30

Peter Bruin11:30-11:55

Johan Bosman12:05-12:30Lunch12:30-3:00

Steve Donnelly3:00-3:25

Aurel Page3:35-4:00

Coffee break4:00-4:30

Ralf Butenuth4:30-4:55

Ariel Martın Pacetti5:05-5:30

Dan Yasaki5:40-6:00

David Loeffler9:00-9:50

Matthew Greenberg10:00-10:50

Coffee break10:50-11:30

Tommaso Centeleghe11:30-11:55

Max Flander12:05-12:30

George Schaeffer12:40-1:05

Lunch1:05-2:00

Excursion2:00-6:00

Boat trip to Neckar-steinach

Meeting points:INF 227 at 2 pm towalk to the terminaltogether, andthe terminal at 2:45pm.

Jan Hendrik Bruinier9:00-9:50

Dan Yasaki10:00-10:50

Coffee break10:50-11:30

Nils-Peter Skoruppa11:30-12:20

Lunch12:20-3:00

Cecile Armana3:00-3:25

Nils-Peter Skoruppa3:35-3:55

Coffee break3:55-4:30

The conference dinner is at the restaurant Backmulde, Schiffgasse 11, at 7:30 pm on Tuesday.

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3.3 Abstracts

Jan Hendrik Bruinier - Coefficients of harmonic Maass forms

The coefficients of half integral weight modular forms are often generating functions of interest-ing arithmetic functions, such as for instance representation numbers of quadratic forms, classnumbers, or central values of integral weight Hecke L-functions. In our talk we consider thecoefficients of half integral weight harmonic Maass forms. We show that their coefficients arerelated to periods of differentials of the third kind on modular and elliptic curves. We presentsome computational results on the coefficients obtained jointly with Fredrik Stroemberg, anddiscuss possible refinements of the relationship to periods.

Xavier Caruso - An algorithm to compute lattices in semi-stable representations

Let K be a finite extension of Qp and GK denote the absolute Galois group of K. In this talk,I will present a polynomial time algorithm to compute a lattice in a semi-stable representationof GK given by its filtered (φ,N)-module. Since p-adic representations attached to classicalor overconvergent modular forms are often semi-stable (and, actually, even crystalline), thisalgorithm applies to such representations and will hopefully, in the next future, help us tounderstand better the behaviour of the semi-simplification modulo p of these representations.The latter question was studied by many people (Breuil, Berger, Buzzard, Gee...) but stillremains very mysterious. It is a common work with David Lubicz.

John Cremona - Modular symbols over number fields

Modular symbols were introduced by Birch and developed systematically by several people,notably Manin and Merel. As well as giving useful theoretical insights into various objectsof interest in arithmetic geometry, such as elliptic curves defined over Q, they are also aninvaluable computational tool: for example, the database of all 1.16 million elliptic curvesover Q with conductor less than 180000 was computed using modular symbols. It is lesswell-known that modular symbols may also be defined and used over number fields otherthan Q; for example, over imaginary quadratic fields so-called Bianchi Modular Forms maybe computed using them.

In this talk I will focus on algebraic properties of modular symbols and the closely relatedManin symbols which may be formulated and proved over quite general number fields, usingstandard algebraic theory of modules over Dedekind Domains. As an application I will exhibita formula for the number of cusps for Γ0(N) where N is an abitrary integral ideal of a numberfield, which generalises the classical formula and give algorithms for testing equivalence ofcusps in this general setting.

This is joint work with Maite Aranes.

Lassina Dembele - Explicit base change and congruences of Hilbert modular forms

Let F be a totally real number field (of even degree). Let E be a subfield of F over which F isGalois. Let n be an integral ideal of F which is stable under Gal(F/E) and k a positive integer.Let Sk(n) be the space of Hilbert modular forms of level n and weight k. We will present an

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algorithm for computing the Hecke submodule of Sk(n) which comes from base change. We alsopresent an algorithm for computing the congruence module of a Hecke submodule M ⊂ Sk(n).We will then use this to investigate a conjecture of Hida on congruences between base changeand non-base change Hilbert modular forms.

Matthew Greenberg - Kneser’s p-neighbour construction and Hecke operators fordefinite orthogonal and unitary groups

In 1957, Kneser introduced the p-neighbour relation on lattices: Lattices L and M are p-neighbours if the elementary divisors of each with respect to the other are p−1, 1, . . . , 1, p. Theconstruction of the p-neighbours of a lattice is completely explicit and can be used to constructrepresentatives for isomorphism classes of lattices in a given genus. In this talk, we relate theKneser’s p-neighbour construction to Hecke operators acting on spaces of automorphic formsfor definite orthogonal groups over totally real fields and for definite unitary groups withrespect to a CM extension. I’ll focus on algorithmic aspects and present examples of ourcomputations. This is a joint project with John Voight.

Alan Lauder - Computations with classical and p-adic modular forms

We present p-adic algorithms for computing Hecke polynomials and Hecke eigenforms associ-ated to spaces of classical modular forms using the theory of overconvergent modular forms.The algorithms have a running time which grows linearly with the logarithm of the weight andare well suited to investigating the dimension variation of certain p-adically defined spaces ofclassical modular forms.

For the paper and related SAGE code see www.maths.ox.ac.uk/~lauder.

David Loeffler - Unitary groups and even Galois representations

I will briefly describe an algorithm for computing the Hecke eigenvalues of automorphic formsfor definite unitary groups, which is discussed in more detail in my lectures in the accompanyingsummer school. I will then describe a method due to Frank Calegari which uses this algorithmto study 2-dimensional even mod p Galois representations, leading to a proof (modulo certainconjectures) that no such representations exist for small weights and levels.

Loıc Merel - Modular forms modulo 2 and modular curves over the real numbers

Let f be a modular newform. Let p be a prime number. Consider the representation ρ :Gal(Q/Q)→ GL2(Fp) attached by Deligne to f and p, and which occurs in Serre’s conjecture.It is odd, in the sense that the image c by ρ of any complex conjugation has determinant −1.When p = 2, there is no distinction between odd and even representations. However, there isstill an alternative: (1) c is the identity or (2) c is a (necessarily unipotent) element of order2 of GL2(F2). In other words, the field extension of Q cut out by ρ is (1) real or (2) not real.

G. Wiese has asked for a method for discerning which case holds using as input only theform f . There is a simple answer to this question. It is based on the Hecke action on modularsymbols. We will see that, in a certain sense, the case (2) is more generic. Most of our work

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will consist in determining the group of components of the jacobians of modular curves overthe real numbers. We will see that this group is small and, in any case, it is ”Eisenstein”.

Nils Skoruppa - Computing modular forms of half integral weight

Dan Yasaki - Computation of certain modular forms using Voronoi Polyhedra

The cohomology of arithmetic groups is built from certain automorphic forms, allowing forexplicit computation of Hecke eigenvalues using topological techniques in certain cases. Formodular forms attached to the general linear group over a number field F of class numberone, these cohomological forms can be described in terms an associated Voronoi polyhedroncoming from the study of perfect n-ary forms over F . In this talk we describe this relationshipand give several examples of these computations resulting from joint work with P. Gunnellsand F. Hajir.

Sara Arias-de-Reyna - On a conjecture of Geyer and Jarden about abelian varietiesover finitely generated fields

Let A be an abelian variety defined over a finitely generated field K. Around 1978 W-D. Geyerand M. Jarden proposed a conjecture concerning the torsion points of A that are defined overcertain infinite algebraic extensions of K. In this talk we will show that this conjecture holdswhen A has big monodromy. This is a joint work with W. Gajda and S. Petersen

Cecile Armana - On Manin’s presentation for modular symbols over function fields

Modular symbols for a congruence subgroup of GL2(Fq[T ]), as introduced by Teitelbaum,have a finite presentation similar to Manin’s for classical modular symbols. We will reporton rather general cases where this presentation can be solved explicitly. The proof does notrequire to know a fundamental domain for the subgroup. We will also present applicationsto L-functions of certain automorphic cusp forms for GL2(Fq(T )) and to Hecke operators onDrinfeld modular forms.

Nicolas Billerey - Explicit Large Image Theorem for Galois Representations at-tached to Modular Forms

In this talk we shall give an explicit version of a large image theorem of Ribet for residualGalois representations attached to classical modular forms (work in progress, joint with LuisDieulefait).

Johan Bosman - Implementation presentation: computing with Galois represen-tations of modular forms

If f is a newform in Sk(Γ1(N)) and λ is a prime of its coefficient field, then there is a mod-λ Galois representation ρ associated with f . Assuming it is irreducible, this representationcan be defined by means of the action of the absolute Galois group on a certain space oftorsion points of a modular Jacobian. We will use SAGE to compute ρ in various cases. Thecomputations rely on numerical approximations of the torsion points mentioned: either over

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the complex numbers or modulo small primes. We will give real-time computations using theformer approach and, if time permits, we will also shed light on the latter approach.

Peter Bruin - Computing in Jacobians of modular curves over finite fields

We describe a collection of algorithms for computing with projective curves over finite fieldsand their Jacobian varieties. We make use of a certain representation of such curves, dueto K. Khuri-Makdisi, which is easy to compute for modular curves. As an application, weexplain how to find (efficiently, at least in theory) an explicit representation for the l-torsionsubscheme of the Jacobian of the modular curve X1(n) over the rational numbers. This is ofinterest for computing Galois representations attached to eigenforms over finite fields.

Ralf Butenuth - On computing quaternion quotient trees

Let K be the rational function field in T over a finite field of q elements. Let Γ be the groupof units of a maximal order in a division quaternion algebra D over K which is split at theplace ∞ = 1/T . Let K∞ denote the completion of K at ∞. Then Γ acts cocompactly onthe Bruhat-Tits tree associated to PGL2(K∞). We present an algorithm for computing afundamental domain for the action of Γ on this tree. This also yields an explicit presentationof Γ. As a Corollary we obtain an upper bound for the size of the generators and their number.

Tommaso Centeleghe - Computing the number of certain Galois representationsmod p

We report on a computational project aimed to find, for a given prime p ≤ 2593, the numberof isomorphism classes of irreducible, two dimensional, odd, mod p, Galois representations ofQ, which are unramified outside p. Serre’s Conjecture reduces the above problem to that ofcounting the number of Hecke eigensystems arising from mod p modular forms of level one.We explain how we succeeded in doing this by only using small index Hecke operators Tn.

Steve Donnelly - Hilbert modular forms in Magma and tables of modular ellipticcurves

This will be a very brief overview of what one can expect from Magma’s Hilbert modularforms (particularily in the forthcoming version of Magma). I’ll also say something about thetechniques used to search for elliptic curves that match Hilbert newforms.

Max Flander - Bases of Modular Forms

The Victor Miller basis is an echelonised basis of q-expansions with integer coefficients for thespace of level 1 modular forms, produced by multiplying powers of the Eisenstein series ofweight 4 and 6, and the unique cusp form of weight 12. We describe a similar procedure forcomputing bases of higher level. and then briefly mention a motivation for these calculations,namely the study of the Newton-slopes of the Hecke operator Up.

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Xevi Guitart - Rational points on elliptic curves over almost totally complexquadratic extensions

Let F be a totally real field containing a field F0 with [F : F0] = 2. Let E/F be a modularelliptic curve which is F -isogenous to its Galois conjugate over F0, and let M/F be an almosttotally complex quadratic extension. In this talk we will discuss a conjectural constructionof points on E rational over M , which builds on a natural extension of Darmon’s theory ofpoints over almost totally real fields. These points are defined by means of suitable integralsof the Hilbert modular form over F0 attached to E by the Shimuara-Taniyama conjecture,which makes the construction amenable for explicit computations and verifications.

Kathrin Maurischat - On Poincare series of low weight for symplectic groups

For the symplectic groups of genus m we study Poincare series of exponential type of weightm+ 1, which are of arithmetic interest. Using representation theoretic techniques we continuethem analytically to the interesting point for m = 2. This continuation involves concreteextensive calculations for Casimir operators. This is manageable by hand only for m ≤ 2.We present the main ideas of these calculations for m = 2 and give some hints for what isrequested for higher genus m to get analog results.

Ariel Martın Pacetti - Hecke-Sturm bound for hilbert modular surfaces

Consider the following problem studied by Hecke: given two modular forms f and g of thesame level and weight, is there an explicit bound N such that if the first N Fourier coefficientsof the two forms are the same, then the two forms are equal? Furthermore, Sturm consideredthe same question modulo a prime ideal, i.e. assume that the Fourier expansion of both formslie in the ring of integers of a number field, and let p be a prime ideal of such ring; is therean explicit constant N such that if the first N Fourier coefficients of both expansions arecongruent modulo p then all of them are congruent?

We will give an algebraic proof of both results and show how to generalize it to Hilbertmodular forms over real quadratic fields.

Aurel Page - Algorithms for arithmetic Kleinian groups

Arithmetic Kleinian groups are arithmetic lattices in PSL2(C). They lie on the boundarybetween number theory and hyperbolic geometry : by Jacquet-Langlands correspondence,their cohomology is closely related to automorphic forms for GL2 over some number fields, andthey act discretely with finite covolume on the hyperbolic 3-space. We present an algorithmwhich computes a fundamental domain and a presentation for such a group, preparing theground for calculating associated automorphic forms. It is a master’s thesis work supervisedby John Voight.

George Schaeffer - The Hecke stability method

I will present a method for producing all weight 1 mod p cusp forms of a given level andcharacter which do not lift to classical weight 1 forms over C.

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4 Practical Information

4.1 Public transport

Summer school and conference are both located on the campus Im Neuenheimer Feld (INF)of the Universitat Heidelberg. The closest tram/bus stop is Bunsengymnasium (Tram 21, 24and Bus 32 from Main Station Heidelberg). Please note that the bus stop Universitatsplatz isat the downtown campus of the university and far away from Im Neuenheimer Feld.

Heidelberg itself is relatively small with a large pedestrian-only zone and plentiful publictransport. It is easy to get around by walking and/or taking public transport. To walk fromthe campus Im Neuenheimer Feld along the Neckar river towards the Altstadt (Old Town) ofHeidelberg takes less than 30 minutes.

Old Town Heidelberg begins east of the station Bismarckplatz with Hauptstraße. Mostbusses and trams go to Bismarckplatz. A single ticket costs 2,20 e for an adult, and a cityticket between Bismarckplatz and Hauptbahnhof (Main station) only 1,10 e (cf. the attachedmaps for more information on prices and connections).

4.2 Hotels

Most participants stay at one of the following hotels:

• Cafe Frisch, Jahnstraße 34, 69120 Heidelberg; Phone: +49 6221 45750. Station: Jahn-straße (Tram 21, 24; Bus 32, 721)

• Gastehaus der Universitat, Im Neuenheimer Feld 370/371, 69120 Heidelberg; Phone:+49 6221 54-7150/-7151. Station: Jahnstraße (Tram 21, 24)

• Hotel Ibis, Willy Brandt Platz 3, 69115 Heidelberg; Phone: +49 6221 9130. Station:Heidelberg Hauptbahnhof (Main Station)

• Hotel Kohler, Goethestraße 2, 69115 Heidelberg; Phone: + 49 6221 970097. Station:Poststraße (Tram 5, 21, 23, 26; Bus 33, 34, 720, 735, 752, 754 ,755; Moonliner 3)

• Hotel Leonardo, Bergheimer Straße 63, 69115 Heidelberg; Phone: +49 6221 5080. Sta-tion: Romerstraße (Tram 22; Bus 32, 35).

• Seminarzentrum der SRH, Bonhoefferstraße 12, 69123 Heidelberg; Phone: +49 62218811. Station: Bonhoefferstraße (Bus 34).

Please see the attached maps or ask at your hotel for further information on how to get to theconference or the summer school.

4.3 Summer School and Conference

Both summer school and conference are located on the campus Im Neuenheimer Feld. Thelectures of the summer school are hold in the lecture hall Horsaal 2 (HS 2) of the buildingMathematisches Institut (INF 288). The independent study groups take place in Horsaal 3/4(HS 3/4) of the same building in the afternoons. The talks of the conference will be in thelecture hall Horsaal 2 of the building Kirchhoff-Institut fur Physik (INF 227).

Registration and coffee breaks will take place in the foyer of the respective lecture hall.

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4.4 Food and Drink

On weekdays, it is most convenient to have lunch on campus: either at the university canteenMensa, or at one of the two reasonably priced restaurants Bellini (see campus map). Duringthe morning coffee breaks, you can purchase a lunch coupon for the Mensa at our registrationdesk for the following prices:

Students Non-StudentsWithout beverage 5 e 7 eWith beverage 6 e 8 e

The coupon is valid at the buffet at “Ausgabe A” (it is not possible to pay in cash in theMensa). For coffee and snacks, there are also the Cafe Chez Pierre in the Mensa building, theUnishop and a bakery next to Bellini (see campus map).

In Old Town Heidelberg, you will find many cafes, restaurants and bars along Hauptstraßefor the evenings and weekends. Restaurants outside Hauptstraße that we recommend are:

• Cafe Bellini, Im Neuenheimer Feld 371, 69120 Heidelberg (Italian cuisine, lower budget)

• Da Claudia, Bruckenstraße 14, 69120 Heidelberg (Italian cuisine, lower budget)

• Dorfschanke, Lutherstraße 14, 69120 Heidelberg (local cuisine)

• Goldener Stern, Lauer Straße 16, 69117 Heidelberg (Greek cuisine)

• Kulturbrauerei, Leyergasse 6, 69117 Heidelberg (local cuisine, brewery and beer garden)

• Merlin, Bergheimer Straße 85, 69115 Heidelberg (Pasta, Schnitzel, salads; lower budget)

• Mocca, Romerstraße 24, 69115 Heidelberg (Mediterranean cuisine)

In addition, the Zeughaus-Mensa (Marstallhof 3, 69117 Heidelberg) of the Universitat Heidel-berg is located beautifully in Old Town. This Mensa offers extended opening hours (Mon-Sat11:30 am-11:00 pm). There it is possible to pay in cash.

For cafes and bars, the Untere Straße is particularily well-known by Heidelberg’s students.Furthermore, the two Marktplatze (market places) in Old Town (adjacent to Heiliggeistkirche)and in Heidelberg-Neuenheim (next to Ladenburger Straße), provide good cafes in great at-mosphere. Worth a visit are for example:

• Max Bar, Marktplatz 5, 69117 Heidelberg.

• Bar Centrale, Ladenburger Straße 17, 69120 Heidelberg.

4.5 Internet Access

Wireless internet is available on the entire campus. Connect to the unencrypted networknamed ”UNI-WEBACCESS” and open any site in a web browser. You will be redirected toa page where you have to enter the user name and password of the conference. Both will becommunicated to you at Heidelberg. Please be aware that this network is unencrypted andshould not be used to transfer sensitive data without additional precautions.

In Old Town, ”UNI-WEBACCESS” is avaibalbe near the old campus at Universitatsplatz.Alternatively, free Wi-Fi is provided at several cafes, e.g. in Untere Straße or in Fahrtgasse(near Bismarckplatz).

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5 Social Program

Wednesday, August 31 - Guided tour

Among the sights in Heidelberg’s Old town are the Church of the Holy Ghost, the Jesuitdistrict and Germany’s oldest university. Our guided tour starts at Universitatsplatz at 4pm, and we will hear interesting facts about Heidelberg and its history. Afterwards we canend the day together at one of the nearby local restaurants.

Saturday, September 3 - Fireworks

To remember the destruction of the castle in 1693, Heidelberg holds castle illuminations threetimes every summer. This saturday is the last time in 2011. Bengal fires will drench the ruinedwalls in a dazzling red light. Subsequently, brilliant fireworks take place at the Old Bridge.We will meet at Bismarckplatz at 9 pm to go near the Neckar river to get the best view.

Sunday, September 4 - Hike

The area around Heidelberg offers many beautiful hikes with pleasant outlooks over the valley.The Heiligenberg mountain is on the other side of the Neckar from the castle and reaches itshighest point at 440 m. The hike starts near the Philosopher’s Walk and proceeds on forestpaths to the Thingsstatte, an amphitheatre built on ancient Greek model during Third Reichfor propaganda purposes. It is possible to proceed to the 548 m high Weißer Stein. Meetingpoint for this hike is the tram stop Bruckenstraße at 11 am.

Tuesday, September 6 - Conference dinner

We will have the conference dinner at the restaurant Backmulde (Schiffgasse 11, http:

//www.gasthaus-backmulde.de) at 7:30 pm on Tuesday. The fee for dinner is 40 e. Itmust be paid at the registration. To reach Backmulde from Bismarckplatz, take Hauptstrasseand make a left at Schiffgasse.

Wednesday, September 7 - Boat excursion

After lunch, we proceed to the shipping terminal. From there we take a boat at 3 pmto Neckarsteinach, a small village on the Neckar river (http://en.wikipedia.org/wiki/Neckarsteinach). The boat trip goes through the beautiful river valley, and finally passesthe four castles of Neckarsteinach. In the village, we can walk along the footpath which leadsto the old ruins, or enjoy the local cafes and restaurants next to the river.

Meeting points are the lecture hall Kirchhoff-Institut fur Physik at 2 pm and theterminal Kongresshaus at 2:45 pm. Please sign up at the registration desk if you want toparticipate.

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6 Heidelberg Sights - Top 10

1 - Schloss (Castle)

The castle is a highlight of any visit, rising majestically over the city and the river.

2 - Alte Brucke (Old Bridge)

This bridge has been an inspiration since the time of the romantic poets.

3 - Hauptstraße (Main Street)

Europe’s longest pedestrian zone has endless shopping, beautiful architecture and museums.

4 - Heiliggeistkirche (Church of the Holy Spirit)

Once home to the Bibliotheca Palatina, this Gothic structure is now Heidelberg’s main Protes-tant church.

5 - Kornmarkt Madonna (Grain Market Madonna)

Try to get a table on Kornmarkt with a view of the Madonna and the castle.

6 - Philosophenweg (Philosopher’s Walk)

One of Germany’s loveliest panoramic trails with outlooks over the city, river, and castle - theHeidelberg triad.

7 - Kurpfalzisches Museum (Electoral Palatinate Museum)

In-depth chronicle of the city and the Palatinate; a must-see for history fans.

8 - Konigsstuhl (King’s Seat)

Heidelberg’s highest peak is accessible by the Bergbahn (Funicular railway) and a good startingpoint for hikes and offers sweeping views of the valley.

9 - Universitatsplatz (University Square)

Here you find historical buildings of Germany’s oldest university town. Worth a visit is alsothe nearby Universitatsbibliothek (University Library).

10 - Explore Heidelberg by Bike

Rent a bike and go to the Tiefburg in Heidelberg-Handschuhsheim, the Palace Gardens inSchwetzingen or along the Neckar river to Ladenburg or Neckargemund.

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7 Participants

Alfes, Claudia (TU Darmstadt)Anni, Samuele (Universiteit Leiden)Arias-de-Reyna, Sara (Universitat Duisburg-Essen)Armana, Cecile (Max-Planck Institut Bonn)Balakrishnan, Jennifer (Harvard University)Banwait, Barinder (University of Wwarwick)Beloi, Alex (University of California, Santa Cruz)Bergamaschi, Francesca (Concordia Un-Paris Sud)Bermudez Tobon, Yamidt (Universitat Heidelberg)Billerey, Nicolas (Universitat Duisburg-Essen)Blanco, Ivan (University of Barcelona)Bley, Werner (LMU Munchen)Bockle, Gebhard (Universitat Heidelberg)Bosman, Johan (University of Warwick)Bruin, Peter (Universite Paris-Sud 11)Bruinier, Jan Hendrik (TU Darmstadt)Butenuth, Ralf (Universitat Heidelberg)Buthe, Jan (Universitat Bonn)Capuano, Laura (Scuola Normale Superiore)Caruso, Xavier (IRMAR Universite de Rennes 1)Centeleghe, Tommaso (Universitat Heidelberg)Cervino, Juan Marcos (Universitat Heidelberg)Cooley, Jenny (University of Warwick)Cremona, John (Univeristy of Warwick)Darmon, Henri (McGill University)Dembele, Lassina (University of Warwick)von Essen, Flemming (University of Copenhagen)Flander, Max (University of Melbourne)Forster, Petra (Karlsruhe Institute of Technology)Greenberg, Matt (University of Calgary)Guitart, Xevi (Universitat Politecnica de Catalunya)Gunnells, Paul (University of Massachusetts)Hoang Duc, Auguste (IRMA Universie de Strasbourg)Hofmann, Eric (Universitat Heidelberg)Inam, Ilker (Uldudag University)Iqbal, Sohail (University of Warwick)Juschka, Ann-Kristin (Universitat Heidelberg)Kazalicki, Matija (University of Zagreb)Kionke, Steffen (Universitat Wien)Krawciow, Karolina (University of Szczecin)Kuhne, Lars (ETH Zurich)Lauder, Alan (Oxford University)Linowitz, Benjamin (Dartmouth College)

15

Loeffler, David (University of Warwick)M’Barak, Saber (Universitat Siegen)Maurischat, Andreas (Universitat Heidelberg)Merel, Loıc (Universite Paris-Diderot)Mohamed, Adam (Universitat Duisburg-Essen)Monheim, Frank (University of Tubingen)Muller, Jan Steffen (Universitat Hamburg)Naskrecki, Bartosz (Adam Mickiewicz University)Nuccio, Filippo A. E. (INDAM-University of Milan)Owen, Mitchell (University of California, Santa Cruz)Pacetti, Ariel Martın (Universidad Buenos Aires)Page, Aurel (Universite Bordeaux 1)Pollack, Robert (Boston University)Purkait, Soma (University of Warwick)Qiu, Yujia (Universitat Heidelberg)Remon, Dionis (Universitat de Barcelona)Ren, Lindsay (Boston University)Restrepo, Juan Ignacio (McGill University)Ruth, Julian (Leibniz Universitat Hannover)Salami, Sajad (Urmia University)Schaeffer, George (University of California, Berkeley)Schimpf, Susanne (Universitat Wien)Sengun, Haluk (Universitat de Barcelona)Shavgulidze, Ketevan (Tbilisi State University)Skoruppa, Nils (Universitat Siegen)Stix, Jakob (Universitat Heidelberg)Tsaknias, Panagiotis (Universitat Duisburg-Essen)Tsukazaki, Kiminori (University of Warwick)Verhoek, Hendrik (Universita’ di Roma)Voight, John (University of Vermont)Vonk, Jan (Oxford University)de Vreugd, Cees (Universiteit van Amsterdam)Wang, Haining (Penn State University)Weigl, Sandra (Universitat Munchen)Wiese, Gabor (Universite du Luxembourg)Yasaki, Dan (University of North Carolina at Greensboro)Zhao, Jingwei (Karlsruhe Institute of Technology)

16

8 Notes

17

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