Geometry and Quantum Theory (GQT)


1 January 2012

Events 2012

Workshop Special Functions and Lie Theory
December 18th, 2012

Speakers: Alberto Grunbaum (UC Berkeley, USA), Paul-Emile Paradan (Montpellier 2, Fr), Pablo Roman (U Nacional Cordoba, Arg), Jasper Stokman (UvA/RU), Wolter Groenevelt (TUD) and Maarten van Pruijssen (RU). PhD-defense of Maarten van Pruijssen on December 19, 2012, 10.30.

2 day seminar – Higher Geometric Structures along the Lower Rhine
December 6th, 2012

This second meeting of the seminar, jointly organised by Bonn (MPI), Nijmegen, and Utrecht, will be held in Nijmegen on December 6th and 7th 2012.

GQT colloquium Amsterdam
November 16th, 2012

place: Universiteit van Amsterdam, Science Park
time: 13:30 – 17:00

13.30-14.30 Oscar Randal-Williams (University of Cambridge): The “Mumford conjecture” package, and applications
14.30-15.00 Coffee break
15.00-16.00 Daniel Huybrechts (Universität Bonn): Old and new problems in the theory of K3 surfaces
16.15-17.15 Geordie Williamson (Max Planck Institut Bonn): Coxeter groups, Kazhdan-Lusztig polynomials and a little Hodge theory

Abstract Randal-Williams:
I will describe how recent work inspired by Madsen and Weiss’ proof of Mumford’s conjecture (on the stable cohomology of the moduli space of Riemann surfaces) gives a conceptual and computational understanding of moduli spaces of Riemann surfaces with extra structure. In particular, I will focus on two interesting examples: the moduli spaces of r-Spin Riemann surfaces, and the universal Picard variety. I will then explain how studying the universal Picard variety leads to a new method for producing tautological relations.

Abstract Huybrechts:
In this talk I will survey a few questions that have been studied intensively for K3 surfaces over the last years. In particular, I will mention rational curves and rational points on K3 surfaces, as well as algebraic cycles and derived categories.

Abstract Williamson:
In 1979 Kazhdan and Lusztig described a remarkably simple yet baffling algorithm to associate a polynomial to any pair of elements in a Coxeter group. Nowadays Kazhdan-Lusztig polynomials play a central role in Lie theory. In this talk I will discuss Coxeter groups and their geometry and describe Kazhdan and Lusztig’s algorithm. I will then discuss some recent work with Ben Elias where we use some ideas from Hodge theory to try to understand these polynomials.

Seminar Elliptic Integrable Systems and Hypergeometric Functions|
October 8th, 2012
Subjects: 1. Elliptic hypergeometric functions 2. Elliptic quantum groups 3. Elliptic integrable lattice models and their interplay. Preparatory seminar for the Lorentz workshop Elliptic Integrable Systems and Hypergeometric Functions (15-19 July 2013). (Tentative) dates: 8/10, 22/10, 12/11, 19/11, 3/12, 17/12 in 3012

Lectures on the unbounded Kasparov product
July 3rd, 2012

Lectures on the unbounded Kasparov product by Adam Rennie (University of Wollongong)
Dates: July 3,5,12,17,19 and 26.
Time: 15:45-17:15
Place: Radboud University Nijmegen, Huygensgebouw, room HG03.632

Workshop Special Functions
June 27th, 2012

One day workshop on Special Functions and related areas. Speakers: Maarten van Pruijssen (Nijmegen), Ana Martinez de los Rios (Seville), Kerstin Jordaan (Pretoria), Kenny De Commer (Cergy-Pontoise), Jasper Stokman (Amsterdam).

GQT colloquium Utrecht
June 1st, 2012

Location: Minnaert building, room 208, Universiteit Utrecht.

13.15-14.15 Jan Denef, Model theory of local fields and toroidalization of morphisms
14.30-15.30 Florian Schätz, de Rham Theorem and higher holonomies
15.30-16.00 Coffee and tea
16.00-17.00 Peter Teichner, Cohomology via field theories
17.00-18.00 Drinks in library Math building

Peter Teichner, Cohomology via field theories
We’ll present results with Stephan Stolz on new relations between algebraic topology and physically motivated notions of field theories.

Jan Denef, Model theory of local fields and toroidalization of morphisms
This talk is about new proofs of some old but celebrated results in the model theory of henselian valued fields. A key example is the Ax-Kochen-Ersov transfer principle that for a given “elementary” assertion about rings we have the following for almost all primes p: the assertion is true in the ring of p-adic integers if and only if it is true in the ring of formal power series over the field with p elements. In the talk we will give an easy proof of this and related results, using a deep result in algebraic geometry, namely the theorem of Abramovich and Karu on toroidalization of morphisms.

Florian Schätz, de Rham Theorem and higher holonomies
I will first sketch an extension of de Rham’s Theorem to an homotopy equivalence of differential graded algebras. This extension allows one to define higher holonomies for graded connections. Then I will indicate how one might use these higher holonomies in order to generalize Tamarkin’s approch to the formality of the little disks operad to higher dimensions (this result was established by Kontsevich via a different approach). The last part is joint work in progress with C. Arias Abad.

Workshop Quantum Groups
March 29th, 2012

There is a one-day workshop Quantum Groups on Thursday, March 29, 2012 with speakers: Martijn Caspers (Radboud U), Kenny De Commer (U Cergy Pontoise, France), Thomas Timmermann (WWU Monster, Germany), Alfons Van Daele (KU Leuven, Belgium).

Workshop “Noncommutative algebraic geometry and its applications to physics”
March 19th, 2012

Topics include: Noncommutative Algebraic and Differential Geometry; Categorical Noncommutative Algebraic Geometry; Moduli Spaces in Noncommutative Geometry; Noncommutative Geometry, and Representation Theory; Applications to String Theory and Quantum Field Theory

Speakers include Yuri Berest, Simon Brain, Lucio Cirio, Alexander Gorsky, Dmitry Kaledin, Ralph Kaufmann, Ludmil Katzarkov, Sebastian Klein, Lieven le Bruyn, Alexander Kuznetsov, Matilde Marcolli, Dmitry Orlov, Goncalo Tabuada, Paul Smith, Vladimir Sokolov, Tom Sutherland, Walter van Suijlekom, Richard Szabo, Jan Jitse Venselaar

Workshop Algebraic Geometry
March 15th, 2012

On the occasion of the thesis defense of Bart van den Dries, a workshop takes place on Thursday, March 15, Room 071 of the Buys-Ballot Building.
The program is as follows:

14:15-14:55 Claire Voisin (Paris): Integral Hodge classes and birational invariants.
15:05-15:55 Slava Kharlamov (Strasbourg): Abundance of real solutions in certain real enumerative problems.
16:15-16:55 Gert Heckman (Nijmegen): On the regularization of the Kepler problem.

Abstract Kharlamov
Surprisingly, in several real enumerative problems the number of real solutions happens to be comparable (for example, in logarithmic scale) with the number of complex ones. Such a phenomenon was first observed in the case of interpolation of real points on a real rational surface by real rational curves (here, the key tool is given by the Welschinger invariants, which can be seen as a real analogue of genus zero Gromov-Witten invariants). In this short talk I will illustrate the same phenomenon by counting real lines (or more generally, real linear subspaces) on nonsingular projective hypersurfaces and their intersections. The key tool in these counts is a kind of real version of Schubert calculus.

Abstract Heckman
We first explain the regularization of the Kepler problem by Moser, and show how the Ligon-Schaaf regularization can be obtained from it in simple terms, as opposed to the original calculational approach by Ligon and Schaaf, even with the simplifications by Cushman and Duistermaat.

GQT colloquium Nijmegen
March 2nd, 2012

Location: Linnaeus building (Heyendaalseweg 137), room LIN 3.
13:00-14:00: Anton Deitmar (Tübingen)
14:00-14:15: Handing out of the GQT master thesis prize
14:30-15:30: Maarten Solleveld (Nijmegen)
15:30-16:00: Coffee/Tea
16:00-17:00: Christopher Deninger (Münster)
17:00-??: Reception

Titles and abstracts
Anton Deitmar
Higher order invariants and non-unitary spectral theory

Symmetry is usually described as invariance under a group action. If the group action is linear, being symmetric is equivalent to being annihilated by the augmentation ideal of the group ring. Higher order invariants of lattices, i.e. elements which are annihilated by higher powers of the augmentation ideal, have in the last decade come into focus in the theory of automorphic forms. They arise in percolation theory and converse theorems. Spectral theory of these has two aspects: varying the lattice via Hecke-theory leads to representations of adele groups, whereas keeping the lattice fixed and varying the representation at the infinite place leads to non-unitary spectral theory. The latter is in general unworkable, but in the situation of lattices in Lie groups there is enough structure around to feed the hope for a nice theory.

Maarten Solleveld
The p-adic Langlands correspondence for the principal series

The local Langlands program aims at the classification of all irreducible representations of reductive groups over local fields. It was set up by Langlands in the sixties and continues to inspire much of the research in this field. Its p-adic branch, also called the p-adic Langlands correspondence, remains conjectural up to this day. It has been established in only a few cases, most noticeably for general linear groups and for irreducible representations in the principal series of split groups. We will discuss the latter, where it comes from and what makes it plausible.

Christopher Deninger
Generalized Nevanlinna theory and invariant measures on the circle

It is well known that real measures on the circle are characterized by their Herglotz transform, an analytic function in the unit disc. Invariance of the measure under N-multiplication translates into a functional equation for the Herglotz transform. Using elements from the theory of Hardy spaces one gets a somewhat surprising condition for a sequence of complex numbers to be the Fourier coefficients of an N-invariant measure. Next, starting from any atomless measure on the circle we construct atomless premesures of bounded kappa-variation in the sense of Korenblum which are invariant under s given pairwise prime integers. The relevant function kappa is a generalized entropy function depending on s. The proof uses Korenblum’s generalized Nevanlinna theory. Passing to “kappa-singular measures” and extending these to elements in a Grothendieck group of possibly unbounded measures on the circle, one obtains generalized invariant measures which are carried by “kappa-Carleson” sets. The range of this construction depends on interesting questions about cyclicty in growth algebras of analytic functions on the unit disc. If there is time, we also discuss some very formal relations with Witt vectors. For example the Artin-Hasse p-exponential “is” a p-invariant premeasure of bounded kappa_1 variation.

Mini symposium in honor of Wilberd van der Kallen
January 20th, 2012

Wilberd van der Kallen will turn 65 in January 2012. The Mathematical Institute of the University of Utrecht and the Geometry and Quantum Theory cluster will celebrate this with a mini symposium in Wilberd’s honor on January 20, 2012 from 13.00-17.00 h. in room 211 of the Minnaert building, de Uithof, Utrecht.

13.15-14.15: Prof. Jean Fasel (Mathematisches Institut der Universität München) Unimodular rows
14.15-14.45: Coffee and tea
14.45-15.45: Prof.Henning Haahr Andersen (Department of Mathematics, University of Aarhus) Tilting modules for reductive algebraic groups
16.00-17.00: Prof. Antoine Touzé (Institut Galilée, Université Paris 13) Frobenius twists in higher invariant theory
17.00-18.30: drinks in the library of the Math building

Afterwards (19.30- ) there is a dinner in the Academiegebouw of the University of Utrecht. If you want to join (approx. 50 euro), please send an e-mail (also indicate if you have diet restrictions or if you want a vegetarian dinner) to both Jan Stienstra and Johan van de Leur ( and before Thursday January 5.

Jean Fasel
Unimodular rows
Let R be a commutative noetherian ring. A projective R-module P is said to be stably free if P⊕Rn≅Rm. By induction, the study of such modules reduces to the case P⊕R≅Rs. Such modules correspond to what is called unimodular rows of rank n. We will survey W. van der Kallen’s work on such rows and then present some recent developments in the subject.

Henning Haahr Andersen
Tilting modules for reductive algebraic groups
Let G be a reductive algebraic group over a field k, e.g. G = GLn(k). In this talk we shall describe the indecomposable tilting modules for G and discuss some of their properties. We will also point to some open problems in representation theory.

Antoine Touzé
Frobenius twists in higher invariant theory
Let V be a representation of the algebraic group GLn(k). If k is a field of positive
characteristic, one can use the Frobenius isomorphism of x→xp to form a twisted representation V(1) of GLn(k). Such representations naturally appear in many problems from representation theory. In this talk we will explain two results where such representations play a crucial role. First they appear in the proof of van der Kallen’s conjecture (now a theorem Touzé, van der Kallen) that reductive algebraic groups have finitely generated cohomology algebras. Second, extensions between such twisted representations also control the cohomology of finite Lie groups (this is a theorem by Cline, Parshall, Scott and van der Kallen). Then we will give some very recent results on the cohomological behaviour of these twisted representations.

Workshop: Higher geometric structures along the Lower Rhine, MPIM Bonn
January 12th, 2012

We would like to announce the first in a series of short workshops on higher geometric structures, jointly organized by the Geometry/Topology groups in Bonn, Nijmegen, and Utrecht, all situated along the Lower Rhine.
The first meeting will be held at the Max Planck Institute for Mathematics, on January 12-13, 2012.

The speakers are:
Dennis Borisov (MPIM Bonn)
Henrique Bursztyn (IMPA, Rio de Janeiro)
David Carchedi (MPIM Bonn)
Mikhail Kapranov (Yale)
Klaas Landsman (Nijmegen)
Stefan Schwede (Bonn)
Chenchang Zhu (Goettingen)