# Events

# Events 2009

**Special day on Lie groups
**

*December 22nd, 2009*

At the occasion of the thesis defense of Vincent van der Noort

**Program**

**Abstracts**: available on website.

**Location**: Buys Ballot Laboratory, 426

**Organizer**: Erik van den Ban

**Thesis defense Vincent van der Noort
**

*December 21st, 2009*

Title: `Analytic parameter dependence of Harish-Chandra modules for real reductive Lie groups — A family affair’

Promotor: E.P. van den Ban

Date, time: Monday, December 21, 14:30

Location: Academiegebouw, Domplein 29

**GQT colloquium Utrecht
**

*December 11th, 2009*

The first lecture of the colloquium will take place in Minnnaertbuilding room 208; lecture 2 and 3 in Minnnaertbuilding room 202.

**Schedule**:

10:50-11:15 Coffee and tea

11:15-12:15 Talk of Alexander Polishchuk

12:15-14:00 Lunch break

14:00-14:05 Student prize Ceremony: Best GQT 2008-2009 M.Sc.-thesis

14:05-15:05 Talk of Ben Moonen

15:05-15:30 Coffee and tea

15:30-15:35 Message from the board of GQT

15:35-16:35 Talk of Boris Dubrovin

16:35-??:?? Drinks

**Abstracts**

**Alexander Polishchuk**

*A-infinity structures on elliptic curves.*

I will show how calculating A-infinity structures on the derived category of coherent sheaves of an elliptic curve leads to new expressions for some classical functions, such as Eisenstein series and Hecke’s indefinite theta series.

**Ben Moonen**

*Chern classes of automorphic bundles *

In my talk I shall discuss tautological classes on compactified Shimura varieties. By definition, the algebra of such classes is generated by the Chern classes of certain natural vector bundles. The picture we have is that for the Shimura variety associated to a pair (G,X) the tautological ring should be isomorphic to the cohomology ring of the compact dual of X, which is a completely explicit ring. We give a simple geometric explanation for this. In cohomology this works. However, on more refined levels (Deligne cohomology, Chow rings) we know this only in special cases and there is a fundamental obstacle that remains. I shall describe where the difficulty lies and will discuss what is known about it. If time permits I will explain how in characteristic p these difficulties can be overcome.

No prior knowledge of the formalism of Shimura varieties is assumed!

**Boris Dubrovin**

*Hamiltonian PDEs and their deformations*

We will explain basic ideas of the deformation theory of Hamiltonian partial differential equations (PDEs), including an introduction to integrable PDEs. In the second part of the talk some properties of solutions to these PDEs will be discussed.

**Talk by Simon Brain (SISSA, Trieste) in Seminar on Quantization, noncommutative geometry and symmetry
**

*December 1st, 2009*

Simon Brain will speak on “The Noncommutative Geometry of Instantons on S^{4}_{&theta}“. Time: 15:45 Location: HG03.084

**2-day workshop “Geometric Aspects of Quantum Theory and Integrable Systems”
**

*October 29th, 2009*

The workshop will take place at the University of Amsterdam, Roeterseiland.

**Thursday; October 29**

**Schedule**

10:15-11:15 N. Reshitikhin, On the large volume limit of random skew plane partitions

11:15-11:30 Break

11:30-12:30 A. Zabrodin, Logarithmic gases and Laplacian growth

12:30-14:00 Lunch break

14:00-15:00 M. Mazocco, Isomonodromic deformations arising in Teichmuller theory

15:00-15:15 Break

15:15-16:15 L. Chekhov, From Teichmuller spaces to Yangian algebras: quantization and reductions

16:15-16:30 Break

16:30-17:30 G. Carlet, The innite dimensional Frobenius manifold associated to 2D Toda hierarchy

**Friday; October 30**

**Schedule**

10:15-11:15 I. Krasil’shchik, Poisson structures in the geometry of PDEs

11:15-11:30 Break

11:30-12:30 S. Loktev, Topological Field Theories for non-orientable Surfaces

12:30-14:00 Lunch break

14:00-15:00 J. S. Caux, Correlations and quenches in integrable systems

15:00-15:15 Break

15:15-16:15 S. Shadrin, A cohomological field theory associated to a TCFT

16:15-??:?? Drinks

Abstracts of the talks are available at the web-page of the workshop at KdVI.

The workshop is organised by **Gerard Helminck** in in collaboration with the Institute for Theoretical Physics.

**GQT colloquium Amsterdam
**

*October 9th, 2009*

The colloquium will take place at the old building of the Korteweg-de Vries Institute (Euclides) at Plantage Muidergracht 24, 1018TV Amsterdam, **Room P.018.**

**Schedule**

10:50-11:15 Coffee and tea

11:15-12:15 Talk of V. Fock

12:15-14:00 Lunch break

14:00-15:00 Talk of A. Alekseev

15:00-15:25 Coffee and tea

15:25-15:30 Message from the board of GQT

15:30-16:30 Talk of J. van de Leur

16:30-??:?? Borrel

**Abstracts
Anton Alekseev**, Geneva

*Associators and their applications*

Drinfeld associators were originally introduced as a tool in the theory of quantum groups. It was later discovered that they play an important role in many fields of mathematics, such as Lie theory, low-dimensional topology, deformation quantization and number theory.

In the talk, we’ll introduce the Drinfeld’s pentagon equation and explain its links to the Kashiwara-Vergne problem in Lie theory and to multiple zeta values in number theory.

**Vladimir Fock**, Strasbourg

*Cluster geometry and quantum theory of higher Teichmueller spaces.*

Ordinary Teichmueller space of complex structures on Riemann surfaces can be viewed as a connected component in the space of homomorphisms of the fundamental group of the surface to the group $SL(2,R)$. Higher Teichmueller space, defined by Hitchin, is a generalisation of this notion in where the group $SL(2,R)$ is replaced by a simple group of higher rank. We shall give an explicit description of this space and discuss its structures: mapping class group action, Poisson structure and quantization.

**Johan van de Leur**, Utrecht

*Givental symmetries of Frobenius manifolds and multi-component KP tau-functions*

We establish a link between two different constructions of the action of the twisted loop group on the space of Frobenius structures. The first construction (due to Givental) describes the action of the twisted loop group on the partition functions of formal Gromov-Witten theories. The explicit formulas for the corresponding tangent action were computed by Y.-P. Lee. The second construction describes the action of the same group on the space of Frobenius structures via the multi-component KP hierarchies. Our main theorem states that the genus zero restriction of the Y.-P. Lee formulas coincides with the tangent KP action. This talk is based on arXiv:0905.0795 wich is a joint publication with Evgeny Feigin and Sergey Shadrin.

**Day on Special Functions
**July 17th, 200

**9**

Speakers: Wolter Groenevelt (TUD), Raimundas Vidunas (Kobe University, Japan), Mizan Rahman (Carleton University, Canada), Tom Koornwinder (UvA)

**The analytic theory of automorphic forms
**

*June 15th, 2009*

A conference at the 65th birthday of Roelof Bruggeman

15-19 June 2009

Speakers include: Eiichi Bannai (Kyushu), Ehud Moshe Baruch (Technion), Kathrin Bringmann (Koln), Roelof Bruggeman (Utrecht), Gautam Chinta (CUNY), Nikolaos Diamantis (Nottingham), Masanobu Kaneko (Kyushu), Emmanuel Kowalski (ETHZ), Winnie Li (Penn State), Anton Mellit (MPIM), Roberto Miatello (Cordoba), Andre Reznikov (Bar Ilan), Morten Risager (Kopenhagen), Akshay Venkatesh (Stanford), Nolan Wallach (UCSD), Don Zagier (College de France/MPIM), Sander Zwegers (UC Dublin).

**Talk by Xiang Tang in Utrecht in the Geometry and Topology seminar
**

*June 9th, 2009*

**Title**: Relative index of CR structures

**Abstract**: We discuss a new proof of the Atiyah-Weinstein conjecture on the index of Fourier integral operators and the relative index of CR structures. This talk is based on a recent joint work with Boutet de Monvel, Leichtnam, and Weinstein.

**GQT colloquium Nijmegen
**

*June 5th, 2009*

**Locatie**: Linnaeusgebouw, zaal LIN 3

**Programme**:

10:45 – 11:00: Koffie/thee

11:00 – 12:00: Giovanni Felder (Zürich): Holomorphic differential operators and Riemann-Roch formulae.

12:00 – 13:30: lunch pauze

13:30 – 13:45: mededelingen van het GQT bestuur

13:45 – 14:45: Tillman Wurzbacher (Metz): On the (hypothetical) Dirac operator on loop space: Topological, geometrical and analytical aspects

15:00 – 16:00: Victor Kac (MIT): Poisson vertex algebras in the theory of infinite-dimensional Hamiltonian equations.

16:00 – : Receptie (Huygensgebouw, bij de wiskunde afdeling).

**Abstract** **Felder’s talk:**

The Riemann-Roch formula extends to a local integral formula for the alternating sum of traces of the action a holomorphic differential operator on sheaf cohomology. In the presence of a compact group action, localization formulae at fixed points are available. The construction is based on ideas of deformation quantization. This is joint work with Markus Engeli and with Xiang Tang based on earlier work with Boris Feigin and Boris Shoikhet.

**Talk by Xiang Tang at the KdV-institute (UvA)
**

*June 4th, 2009*

11.00, Room A1.06, Sciencepark 904 (the new location of the KdV institute!)

**Title**: Hochschild cohomology of orbifolds and Dunkl operators

**Abstract**: We will explain how Dunkl operators show up in the study of Hochschild cohomology of orbifolds. After that, we plan to discuss an approach to use Dunkl operators to construct some “new” deformation quantizations of orbifolds.

**Lecture by M. Lehn
**

*April 29th, 2009*

**Title**: Holomorphic symplectic varieties

**Location**: KdV Institute, UvA, room P.014 Time: 11:15 – 12:00.

**Seminar on Modular Forms
**

*April 17th, 2009*

14:00-14:50 Matthias Schuett (University of Copenhagen)

*K3 surfaces and modular forms*

15:00-15:50 Gerard van der Geer (University of Amsterdam)

*Siegel modular forms of low genera*

16:00 Coffee/Tea

16:30-17:20 Don Zagier (MPIM Bonn/ CdF Paris)

*On a U(3,1)-automorphic form of Ferapontov-Odesskii*

18:00 Dinner

**G. Laumon: The weighted fundamental lemma
**

*April 3rd, 2009*

Two lectures (joint work with P.-H. Chaudouard)

15:00 – 16:00

16:30 – 17:30 KdV Institute, UvA, room P 0.14

**DIAMANT – GQT colloquium
**

*March 20th, 2009*

**Schedule**

10.45.00-17.00 h. in Minnaertgebouw 208, Universiteit Utrecht:

10.45-11.00 coffee and tea

11.00-12.00: Spencer Bloch, Algebraic geometry associated to graphs

12.00-13.15: Lunch

13.15-14.15: Alex Quintero Velez, McKay correspondence for Landau-Ginzburg models

14.30-15.30: Rob de Jeu, K4 of curves over number fields

15.30-16.00: Tea and coffee

16.00-17.00: Dmitri Orlov, Triangulated categories of singularities, D-branes in LG-models and mirror symmetry

17.05- : Drinks in the library of the Mathematical Institute

**Abstracts
Spencer Bloch**

*Algebraic geometry associated to graphs*

The Feynman amplitude associated to a graph in physics is a period of the hypersurface defined by the Kirchoff polynomial, a classical invariant of the graph. I will explain work on the “motive” of the graph.

**Alex Quintero Velez**

*McKay correspondence for Landau-Ginzburg models*

The McKay correspondence is a principle that relates the geometry of a resolution of singularities of a quotient variety M/G and the equivariant geometry of the group action. The classic case is McKay’s identification of the cohomology of the resolution of a Kleinian singularity CC2/G with the representation theory of G. In this talk, we discuss an analogue of the McKay correspondence for Landau-Ginzburg models. This leads naturally to a generalized notion of the McKay correspondence as an isomorphism of “noncommutative spaces” (in Kontsevich’s sense).

**Rob de Jeu**

*K4 of curves over number fields*

We give a conjectural description (due to Goncharov) of K4 modulo torsion of a curve over a number field, using certain complexes based on the function field of the curve. We also discuss to which extent this has been proved. Furthermore, we illustrate a method of finding non-zero examples for elliptic curves E defined over Q, and numerically verify the relation between their regulators and L(E,3) predicted by the Beilinson conjectures. The latter is joint work in progress with Sander Meinema.

**Dmitri Orlov**

*Triangulated categories of singularities, D-branes in LG-models and mirror symmetry*

I am going to talk about triangulated categories of singularities and categories of D-branes of type B in Landau-Ginzburg models and sigma-models. Different properties of these categories will be described. At the end of my talk I am also going to discuss mirror symmetry and a generalized strange Arnold duality.

**Thesis defense Alex Quintero
**

*March 2nd, 2009*

Thesis: Equivalence of D-Brane Categories

Author: Alexander Quintero Velez

Promotor: Hans Duistermaat, copromotor: Jan Stienstra

Date/Time: Monday 2/3-2009, 12:45

**Math-Physics seminar
**

*February 27th, 2009*

Lectures from 14:00 – 16:30, Buys Ballot 276, followed by drinks

**Speakers:
**

**Andrew Dancer**(Oxford, U.K.)

*Ricci solitons with large symmetry group*

We use dynamical systems methods to produce new examples of Ricci solitons, including some not of Kahler type.

**Maxim Zabzine** (Uppsala, Sweden)

*Generalized geometry and chiral de Rham complex*

Chiral de Rham complex is the way to associate the conformal field theory to a curved target space. I will briefly review the ideas behind the chiral de Rham complex. I will discuss the relation between chiral de Rham complex and the generalized geometry. I will conclude with the brief comments on the applications

(organizers: Bernard de Wit, Eduard Looijenga, Jan Stienstra, Stefan Vandoren)

**GQT colloquium at Amsterdam
**

*February 6th, 2009*

The speakers are Arthur Bartels (Univ. of Muenster), Ezra Getzler (Northwestern Univ.), and Jasper Stokman (Univ. of Amsterdam).

**Schedule**

10:45 – 11:00: Coffee and tea

11:00 – 12:00, Room P 0.14: Ezra Getzler.

12:00 – 13:30: Lunch

13:30 – 14:30, Room G.S.04: Arthur Bartels.

14:30 – 14:45: Coffee and tea

14:45 – 15:45, Room G.S.04: Jasper Stokman.

16:00 – ??:??, Euclides canteen: Reception

**Abstracts**

**Ezra Getzler**

*Gerbes and supergravity
*Four-dimensional supergravity is a classical field theory involving the addition of a matter field, called the Rarita-Schwinger field, to Einstein’s theory of gravitation. The local covariance exhibited by Einstein’s theory (in contemporary language, equivariance under the action of the Lie algebra of vector fields) is generalized in supergravity to the action of a Lie superalgebra; this symmetry is called local supersymmetry.

By contrast with the situation in the theory of gravity, the supersymmetry of supergravity is not exhibited at the level of the field equations, but only on the space of solutions of these equations; physicists say that supersymmetry only holds “on-shell”. There is an equivalent formulation of supergravity, involving the addition of a pair of new fields, a Hermitian connection A on a complex line bundle and a two-form B, such that the resulting theory exhibits supersymmetry “off-shell”, even before imposing the equations of motion; this theory, introduced by Sohnius and West, is called “new minimal supergravity”.

In this talk, we interpret the two-form as the curving of a gerbe, and the coupling between the fields A and B in terms of Beilinson’s product on Deligne cohomology. This permits the definition of new minimal supergravity not just on domains of Minkowski space, but on manifolds.

Applying this formalism to the double of a manifold with boundary, we explain how to formulate new minimal supergravity in the presence of a boundary. (Here, we are expanding on a discussion by Lambert and Moore.) Here, Z/2-equivariant gerbes make their appearance.

One of the goals of this talk is to offer an introduction to gerbes and their geometry – little background beyond familiarity with differential forms and connections on line bundles will be assumed

**Arthur Bartels**

*Hyperbolic groups and aspherical manifolds*

An aspherical manifold is a closed manifold whose universal cover is contractible. Up to homotopy such a manifold is determined by its fundamental group. Borel conjectured that such a manifold is in fact determined up to homeomorphism by its fundamental group. It is also of interest to determine which groups arise as fundamental groups of aspherical manifolds. I will discuss these questions for word-hyperbolic groups in the sense of Gromov.

**Jasper Stokman**

*Affine Hecke algebras and bispectral quantum KZ equations*

I first review the role of the affine Hecke algebra H in the construction of quantum invariants of braids and ribbon tangles in a thickened cylinder, as well as its application in integrable models of statistical mechanics. Much of the relevant information is stored in an explicit H-valued cocycle of the associated Weyl group, which depends on a set of spectral parameters as well as on a set of twisting parameters. The twisting parameters encode the choice of boundary conditions for the associated integrable models.

In the second part of the talk we come to the central object of the talk: the quantum KZ equations. They form a holonomic system of difference equations acting on spectral parameters. They are solved by correlation functions of the above mentioned integrable models. I establish a holonomic extension of the quantum KZ equations by exhibiting an explicit compatible system of difference equations acting on twisting parameters. I discuss its application in creating symmetric Laurent polynomial solutions of quantum KZ equations. This class of solutions is of particular interest due to its connection with Macdonald polynomials, and its application to the Razumov-Stroganov conjecture. This is joint work with Michel van Meer.

**Oratie Gunther Cornelissen
**

*January 16th, 2009*

Tijdstip: 16.15; locatie: Academiegebouw, Domplein, Utrecht