Geometry and Quantum Theory (GQT)


1 April 2010

Events 2010

Seminar on geometry and topology (UU)
December 20th, 2010

Date: Monday 20 December
Place: room 611, Mathematics Building, Utrecht

11:00-12:00: Hessel Posthuma (Amsterdam)
Integrable hierarchies and Frobenius manifolds

15:00-16:00: Julie Bergner (UC Riverside)
Generalized classifying space constructions

16:30-17:30: Christian Blohmann (Regensburg/Bonn)
Homotopy equivalence of correspondences and anafunctors of higher groupoids

Abstracts can be found on the website

GQT colloquium
December 10th, 2010

Frederic Bourgeois (Bruxelles)
Holomorphic curves in contact geometry
Holomorphic curves were introduced in symplectic geometry by Gromov. These rapidly proved to be extremely valuable tools to study symplectic rigidity and to construct symplectic invariants. The goal of this talk is to explain how these techniques can also be applied to contact geometry, with a focus on contact homology, a holomorphic curves invariant for contact structures. This will be illustrated with several examples and some selected results.

Walter van Suijlekom (Nijmegen)
Gauge theories and noncommutative manifolds
In this talk, we will discuss some aspects of the intrinsic gauge theoretical nature of noncommutative manifolds. Following Connes, we descibe a noncommutative (Riemannian, spin) manifold by its fundamental class in K-homology. Among other functional analytical data, such a K-cycle consists of a (noncommutative) C*-algebra. As a consequence of noncommutativity, there might exist non-trivial inner automorphisms; these will be referred to as gauge transformations. The key example that motivates this terminology from physics is when one replaces the algebra of functions on a manifold by matrix-valued functions. The resulting Morita equivalence describes ordinary Yang-Mills theory as formulated in terms of connections on principal bundles. As another class of examples, we will discuss deformations of a manifold along a torus action, first introduced by Rieffel. The noncommutative algebra turns out to contain a commutative subalgebra, corresponding to functions that are constant along the orbits of the torus (and hence remain undeformed). We will present a novel interpretation of the noncommutative K-cycle as describing a gauge theory on the (commutative) orbit space. The gauge theory naturally involves connections on Hilbert bundles on this background manifold. If time permits, we formulate a decomposition in Kasparov’s KK-theory that captures this and the above example.

Ilia Itenberg (Strasbourg)
Tropical geometry and enumeration of real rational curves
The purpose of the talk is to make an introduction to tropical geometry with an emphasis on applications of tropical geometry in complex and real algebraic geometries. Tropical geometry has deep relations with many branches of mathematics. In good cases, a tropical variety is approximated by a one-dimensional family of complex varieties. This gives rise to important links between the complex algebraic world and the tropical one. One of the links is given by Mikhalkin’s correspondence theorem. This theorem, together with Welschinger’s discovery of a real analog of genus zero Gromov-Witten invariants, produces new results on enumeration of real rational curves. We will also discuss tropical homology groups which carry an important information about a degenerating one-dimensional family of complex varieties.

10:50-11:15 Coffee and tea (outside LIN 6)
11:15-12:15 Talk of F. Bourgeois (LIN 6)
12:15-13:45 Lunch break
13:45-14:45 Talk of W. van Suijlekom (LIN 3)
14:45-15:00 Messages from the GQT board, awarding of the GQT master thesis prize, discussion of GQT programme MasterMath
15:00-15:20 Coffee and tea
15:20-16:20 Talk of I. Itenberg (LIN 3)
16:30-??:?? Borrel (Huygensbuilding)

All talks will take place in the Linnaeus building (Heyendalseweg 137), but in different rooms for morning and afternoon sessions.

GQT colloquium
October 8th, 2010

The colloquium will take place at Science Park 904, 1098 XH Amsterdam, room A1.04. The speakers are Tilman Bauer (VU Amsterdam), Viatcheslav Kharlamov (IRMA, Strasbourg), and Robert Penner (Aarhus Univ. and Caltech).

10:30 – 11:00: Coffee and tea.
11:00 – 12:00: Talk of Robert Penner.
12:00 – 14:00: Lunch.
14:00 – 15:00: Talk of Viatcheslav Kharlamov.
15:00 – 15:30: Coffee and tea.
15:30 – 16:30: Talk of Tilman Bauer.
16:30 – ??:??: Reception

Titles and abstracts
Tilman Bauer
Unstable operations in Morava K-theory
The Morava K-theories are a familiy of homology theories which are singled out among other homology theories by the fact that they behave analogously to the prime fields $\mathbb{F}_p$ among all abelian groups. I will show how these can be used effectively to compute the homotopy groups of a space (or, more precisely, of a localization of a space) using an Adams-type spectral sequence.

Viatcheslav Kharlamov
First steps in enumeration of real rational curves on surfaces. Welschinger invariants, their definitions and properties
Welschinger invariants is a real analogue of genus zero Gromov-Witten invariants. Their general theory is still under construction but they gave already a number of non-trivial applications, especially in real enumerative geometry where they remain the main source of lower bounds on the number of real solutions (one may mention as one of the first applications of the Welschinger invariants a proof of the existence of real solutions in the problem of interpolating real points by real rational plane curves of given degree). In this talk, based on joint works with I. Itenberg and E. Shustin, I will remind how Welschinger invariants look like in the case of surfaces, point certain modifications, and then concentrate on some basic properties (like positivity, monotonicity and asymptotic growth) obtained in the case of Del Pezzo surfaces (with $K2\ge 3$ for the moment) by means of real analogues of Caporaso-Harris type recursive formulas.

Robert Penner 
Protein and RNA Moduli Spaces 
Several joint projects with J. E. Andersen and others have applied techniques and results from moduli spaces to various problems in proteomics and genomics. Protein has its characteristic geometric structure, which is naturally modeled using spaces of SO(3) graph connections, leading to a nice notion of protein moduli space. In genomics, the geometry is less well understood, in part because of the dearth of data, but the combinatorics nevertheless remains useful: Earlier joint work with M. S. Waterman had analyzed moduli spaces of all possible unknotted RNA secondary structures using planar fatgraphs, and current joint work with JEA, MSW, and C. M. Reidys goes beyond this towards solving the problem of enumerating all possible knotted RNA secondary structures of a specified topology with its concomitant applications to the RNA folding problem.

Symposium on quantum probability and quantum information
October 5th, 2010

Place: Minnaertbuilding room 023, de Uithof, Utrecht

11:00-12:00: Hans Maassen
Introduction to quantum probability and quantum information
(lunch break)
13:00-14:00: Nilanjana Datta
Relative entropies and entanglement monotones
14:15-15:15: Mark Fannes
Entropic bounds for correlated states
(tea break)
15:45-16:45: Madalin Guta
Fisher information and asymptotic normality for quantum Markov chains

If you want to attend, please send an e-mail to:

Promotie Bas Janssens
October 4th, 2010

Titel Proefschrift: Transformation & Uncertainty (Some Thoughts on Quantum Probability Theory, Quantum Statistics, and Natural Bundles)

Academiegebouw Utrecht, Domplein 29, Utrecht
Aanvang 14.30 uur

GQT conference: 28/6 – 2/7, 2010. Registration open.
June 28th, 2010

Conference at the occasion of the fourth year of existence of the GQT cluster.

  • Monday 28/6 – Thursday 1/7: Nijmegen
  • Friday 2/7: awardance of Compositio Prize, Amsterdam (UvA)
  • More details: see conference website

    G. Felder lectures
    June 9th, 22th, 24th, 2010

    Giovanni Felder from ETH in Zurich will be the guest of the Mathematics Department of the Radboud University Nijmegen from June 8 until July 3 of this year, as visiting GQT-professor.

    He will give a general colloquium lecture on

  • Wednesday June 9, 11-12 in lecture room HG00.062:
    Gaudin models, the symmetric group and stable rational curves.
  • This lecture is intended for a general mathematical audience.

    There will be two days of lectures the week before the GQT-conference. On both of these days we intend to have dinner in town with the speakers and the audience of the lectures. If you are interested, please join us.

    Tuesday June 22 in HG00.062 of the Huygens Building:

  • Jochen Heinloth (11:15-12:15 & 13:45-14:30):
    An example of the geometric Langlands correspondence with wild ramification.
  • Giovanni Felder (14:45-15:45 & 16-17) Quantum Calogero-Moser systems on elliptic curves I.
  • Thursday June 24 in HG00.071 of the Huygens Building:

  • Jasper Stokman (11:15-12:15 & 13:45-14:30):
    Cherednik algebras, KZ equations and Bispectrality.
  • Giovanni Felder (14:45-15:45 & 16-17):
    Quantum Calogero-Moser systems on elliptic curves II.

  • GQT colloquium Utrecht
     June 4th, 2010

    Place: Minnaert building room 208, Utrecht

    10:50-11:15 Coffee and tea
    11:15-12:15 Talk of Yan Soibelman
    12:15-14:00 Lunch break
    14:00-15:00 Talk of Gert Heckman
    15:00-15:25 Coffee and tea
    15:25-15:30 Message from the board of GQT
    15:30-16:30 Talk of Alexei Davydov
    16:45-??:?? Drinks in Library Math building

    Yan Soibelman
    Motivic Donaldson-Thomas invariants and cluster transformations.
    In a joint work with Maxim Kontsevich we introduced motivic Donaldson-Thomas invariants of 3-dimensional Calabi-Yau categories. Such a category can be associated e.g. with a quiver with potential. Mutation of the quiver with potential corresponds to a change of t-structure of the Calabi-Yau category. Comparing motivic DT-invariants calculated in those two t-structures we arrive to the quantum cluster transformation of the quantum torus naturally associated with the Grothendieck group of the category. I am going to explain this result with the necessary preliminaries.

    Gert Heckman
    Hyperbolic Structures and Root Systems
    We discuss the construction of a one parameter family of complex hyperbolic structures on the complement of a toric mirror arrangement associated with a simply laced root system. Subsequently we find conditions for which parameter values this leads to ball quotients.

    Alexei Davydov:
    Witt group of modular categories (joint with A. Kitaev, M. Mueger, D. Nikshych, V. Ostrik)
    We describe an abelian group structure on the set of classes of modular categories modulo some equivalence relation. The resulting Witt group of modular categories resembles (and contains) the Witt group of finite abelian groups with quadratic forms. The conjecture of Moore and Seiberg, that all RCFTs come from reductive groups via WZW, coset and orbifold constructions, can be interpreted as a statement about generators of this Witt group.

    Master Class “Geometry of Gauge Theories and Geometric Quantization”
    May 31st, 2010

    This master class will be held at the University of Amsterdam (at the science park) from May 31 — June 11, 2010 and is also suitable for master students (4 credit points).
    Lectures by N. Reshetikin and J.E. Andersen.
    Further information may be obtained from the website, where one can register for the master class (registration deadline is March 29th).
    Information may also be requested at

    Talk by Pablo Roman (KU Leuven) in Mathematical Physics Seminar.
    May 4th, 2010

    Title: Matrix valued orthogonal polynomials, spherical functions and the hypergeometric operator. Time and place: Tuesday May 4, 2010 (9:30-10:30) in room HG03.084

    Lecture O. Garcia-Prada
    April 27th, 2010

    O. Garcia-Prada (CSIC Madrid/MPI Bonn) will give a talk at the UvA:
    Title: Involutions of the moduli space of Higgs bundles and real forms
    Abstract. We consider involutions of the moduli space of G-Higgs bundles over a compact Riemann surface, where $G$ is a complex reductive Lie group, and study the relation of the fixed points subvarieties with representations of the fundamental group of the surface into real forms of G.
    Room: A1.04, Science Park Amsterdam
    Time: 16:00-17:00

    Masterclass W. van Suijlekom (RU Nijmegen)
    April 26th, 2010

    W. van Suijlekom (RU Nijmegen) will give a “masterclass in the masterclass” at Utrecht, 26-29 april: Noncommutative geometry and physics Time: 9-11 on Mon 26/4, Wed 28/4 and Thu 29/4; Location: WIS611, Everybody welcome! Priority to MRI-masterclass students

    GQT colloquium Leiden
    April 16th, 2010

    The GQT colloquium will be the last day of the MRI/GQT conference The Interface of Integrability and Quantization which will be held at the Lorentz Center from 12 Apr 2010 through 16 Apr 2010.

    Masterclass C. Consani (JHU): 15-17 March: Around the field with one element
    March 15th, 2010

    C. Consani (Johns Hopkins) will give a “masterclass in the masterclass” lecture 15-17 March: Around the field with one element, Time: Mon 15/3, 9-12 and Wed 17/3, 9-11; Location: BBL005, Everybody welcome! Priority to MRI-masterclass students

    Masterclass G. Robertson (Newcastle): 1-5 March: Noncommutative geometry of euclidean buildings and their boundaries
    March 1st, 2010

    Guyan Robertson (Newcastle) will give a “masterclass in the masterclass” lecture at Utrecht ,1-5 March: Noncommutative geometry of euclidean buildings and their boundaries, Time: 9-11, Locations: Mon 1/3 in BBL005, Wed 3/3, Thu 4/3, Fri 5/3: WIS611 Everybody welcome! Priority to MRI-masterclass students

    GQT colloquium Amsterdam
    February 12th, 2010

    The colloquium will take place at the new building of the FNWI at Science Park 904, 1098XH Amsterdam, Room A1.10.

    10:50-11:15 Coffee and tea
    11:15-12:15 Talk of S. Bloch
    12:15-14:00 Lunch break
    14:00-15:00 Talk of M.-T. Benameur
    15:00-15:25 Coffee and tea
    15:25-15:30 Message from the board of GQT
    15:30-16:30 Talk of M. Crainic
    16:30-??:?? Borrel

    Spencer Bloch, Chicago
    Introduction to iterated integrals and multiple zeta-numbers.
    (Relativistic) Quantum Field Theory is a rich source of fascinating problems in algebraic geometry. In this lecture I will outline some general questions involving physics and algebraic geometry (motives).
    I. Iterated integrals; multiple zeta-numbers.
    II. Graphs; Feynman rules; Feynman amplitudes; Feynman parameters.
    III. External momenta and masses.
    IV. Renormalization; limiting mixed Hodge structures.
    V. Monodromy; Cutkowsky Rules.

    Moulay-Tahar Benameur, Metz
    The foliated Cheeger-Gromov invariant
    We shall review the classical rho invariant and introduce the foliated rho invariant associated with a holonomy invariant measure on a smooth closed odd foliation. Then we shall explain a foliated homotopy invariance theorem for the signature operator.

    Marius Crainic, Utrecht
    Local forms in Poisson geometry
    I will report on recent joint work with Ionut Marcut (PhD student, UU) on a Poisson geometric version of the slice theorem (in equivariant geometry) and of the local Reeb stability (in foliation theory). This theorem is a generalization of Conn’s linearization theorem- a generalization which is possible due to recent geometric proof (joint with R.L. Fernandes) of Conn’s theorem. I will spend most on the time on recalling the classical results, explaining the result and looking at examples. If time allows, some ideas of the proof will be given.

    Stieltjes Onderwijsweek 2010
    January 25th, 2010

    From 25 till 28 January 2010 a “Stieltjesonderwijsweek” will take place at the VU, mainly aimed at PhD students and postdocs. It will provide a good background for the talks of Spencer Bloch as Stieltjes professor during February and March 2010, but the chosen subjects are of independent interest in algebraic geometry and related fields. It gives an introduction to the following topics * Cohomology theories * Mixed Hodge structures and their variations. * Local systems and monodromy.

    Organizers: Bas Edixhoven, Rob de Jeu, Ben Moonen, Tejaswi Navilarekallu, Jan Stienstra, Lenny Taelman.

    For more details see site.