Geometry and Quantum Theory (GQT)


1 April 2009

Events 2009

Special day on Lie groups
December 22nd, 2009

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


  • 10:15 – 11:05: Bernhard Kroetz (Hannover): Analytic factorization of Lie group representations
  • 11:15 – 12:05: Eric Opdam (Amsterdam, UvA): Hecke algebras and the tempered L-function conjecture
  • 13:30 – 14:20: Henrik Schlichtkrull (Copenhagen): Analytic representations of Lie groups
  • 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.

    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

    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 S4&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
    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
    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.

    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

    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, 2009

    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

    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

    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

    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

    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).

    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

    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