This is the sixth workshop that we are organizing. These mini-workshops take place biannually. The goal is to strengthen the symplectic community of the Netherlands and to connect it with abroad. Topics include Hamiltonian dynamics, the symplectic embedding question, holomorphic curves, and Floer homology.

* If you are interested in participating then please register.

Kaoru Ono (Kyoto)

Sergei Kuksin (Paris 7)

Peter Albers (Heidelberg)

Alberto Abbondandolo (Bochum)

Oliver Fabert (Vrije Universiteit Amsterdam)

Fabian Ziltener (Universiteit Utrecht)

Tuesday the 17th and Wednesday the 18th of December on the occasion of Qizheng Yin’s defence of his doctors thesis.

The defence will be on the Wednesday.

**Speakers (December 17th)**

Gerard van der Geer (Amsterdam)

Dan Petersen (Zürich)

Arnaud Beauville (Nice)

Qizheng Yin (Nijmegen)

**Speakers (December 18th)**

Lenny Taelman (Leiden)

Claire Voisin (École Polytechnique)

Sergey Shadrin (Amsterdam)

**Belgian-Dutch Algebraic Geometry Day
**

**Venue**

The lectures are given in the Huygens Building, room HG00.071 on the ground floor.

Address: Heyendaalseweg 135, Nijmegen.

**Programme**

13:00-14:00 Nero Budur (Leuven) TBA

14:00-14:30 Coffee break

14:30-15:30 Stefan Schröer (Düsseldorf) TBA

15:30-16:00 Coffee break

16:00-17:00 René Schoof (Rome) TBA

As usual, after the lectures we intend to go for an informal dinner in town.

**Workshop on Foliations and Orbispaces, 21-22 November
**

**Description**

The focus of this short workshop lies on (possibly singular) foliations are their leaf spaces, both from a classical perspective (\Gamma-structures, Riemannian foliations,..) and a modern one (Lie groupoids).

**Speakers**

Gael Meignez (Bretagne-Sud)

Marcos Alexandrino (Sao Paulo)

Hessel Posthuma (Amsterdam)

Matias del Hoyo (Utrecht)

Marco Zambon (Madrid)

**Higher Geometric Structures along the Lower Rhine III
**

This is the third in a series of short workshops jointly organized by the Geometry/Topology groups in Bonn, Nijmegen, and Utrecht, all situated along the Lower Rhine. The focus lies on the development and application of new structures in geometry and topology such as Lie groupoids, differentiable stacks, Lie algebroids, generalized complex geometry, topological quantum field theories, higher categories, homotopy algebraic structures, higher operads, derived categories, and related topics. The first workshop took place in Bonn and the second in Nijmegen.

**Speakers **

Camilo Arias Abad (Bonn)

Javier Gutiérrez (Nijmegen)

Matias del Hoyo (Utrecht)

Arturo Prat-Waldron (Bonn)

Gregor Schaumann (Universität Erlangen-Nürnberg)

Pavol Ševera (Université de Genève)

Anton Zeitlin (Columbia University)

**Workshop Noncommutative Geometry and Particle Physics, Leiden\
**

Lorentz Center Leiden, October 14-18, 2013.

**Topics:**

- The Higgs Sector and its Experimental Status
- Phenomenology of Electroweak and Strong Forces
- The Noncommutative Standard Model
- Particle Physics: Beyond the Standard Model
- Family Structure of Particle Physics
- Gravity and Noncommutative Geometry

**Scientific organizers:**

- Thijs Van den Broek (Nijmegen, The Netherlands)
- Alain Connes (Bures-sur-Yvette, France)
- Jose Gracia-Bondia (Zaragoza, Spain)
- Piet Mulders (Amsterdam, The Netherlands)
- Walter Van Suijlekom (Nijmegen, The Netherlands)

**Workshop Knots & Physics, Amsterdam
**

**Speakers:**

Gaetan Borot (MPI Bonn),

Jinseok Cho (KIAS Seoul),

Sebas Eliens (ITF Amsterdam),

Hitoshi Murakami (Tohoku University),

Satoshi Nawata (NIKHEF Amsterdam).

**Organisers:** Satoshi Nawata and Roland van der Veen

**Workshop “Elliptic Integrable Systems and Hypergeometric Functions”
**

5 day workshop from July 15th – 19th, 2013. Scientific organizers: Erik Koelink, Masatoshi Noumi, Eric Rains, Hjalmar Rosengren, Simon Ruijsenaars, Jasper Stokman.

**A singular life – Conference in honour of Eduard Looijenga
**

This two-day conference (27 & 28 of June) marks the retirement of Professor Eduard Looijenga and will be a celebration of his achievements and influence in Dutch and International mathematics. The confirmed speakers are Arnaud Beauville (Laboratoire J.-A. Dieudonn�, Nice), Igor Dolgachev (University of Michingan), Carel Faber (Royal Institute of Technology, Stockholm), Gerard van der Geer (University of Amsterdam), Gert Heckman (Radboud Universiteit Nijmegen), Joseph Steenbrink (Radboud Universiteit Nijmegen), Jonathan Wahl (University of North Carolina), Shing-Tung Yau (Harvard University) Don Zagier (Max Planck Institute — Bonn)

**G&T day – Utrecht
**

The Quarterly seminar on Topology and Geometry aims to take place every bimester in the mathematics department in Utrecht. Our next meeting will happen on the 21st of June 2013 in MIN 211.

The speakers will be Jonny Evans, Igor Khavkine and James Tener.

**Mini Workshop on locally analytic representations and some applications
**

June 5-6, 2013, at Vrije Universiteit Amsterdam

supported by the DIAMANT cluster*

**Organizers:** Deepam Patel (VU Amsterdam), Tobias Schmidt (Munster), Matthias Strauch (Indiana)

* funded by the Netherlands Organisation for Scientific Research (NWO), the Ministry of Education, Culture and Science (OCW), and the Ministry of Economic Affairs (EZ).

**Topology & Geometry Day on the occasion of Maria Amelia Salazar’s Ph.D. defense
**

**GQT colloquium Utrecht
**

Place: Universiteit Utrecht; Minnaert Building, room 208.

Schedule: 13:00 to 14:00 – Kim Froyshov (Aarhus): On the existence of representations of finitely presented groups in compact Lie groups;

14:00 to 14:30 – Coffee;

14:30 to 15:30 – Moritz Groth (Nijmegen): Some first steps with Grothendieck derivators;

15:45 to 16:45 – Matthias Kreck (Hausdorff Institute): Special codes – special manifolds?

**Workshop “Moduli of curves and integrable hierarchies”
**

On the occasion of the thesis defense of Alexandr Buryak, a workshop takes place on Friday, April 26 at the University of Amsterdam (Plantage Muidergracht 24, 1018 TV Amsterdam, N.B.: This is OLD LOCATION of the KdV Institute). The lecture room is P0.14.

The **program** is as follows:

13:15-14:15 Maxim Kazarian (Moscow): Topological recursion for the genus zero descendant Hurwitz potential.

14:15-14:45 Coffee and tee.

14:45-15:45 Johan van de Leur (Utrecht): Hirota equations for the extended bigraded Toda hierarchy and the total descendant potential of CP^1 orbifolds.

16:00-17:00 Dimitri Zvonkine (Paris): A (complete?) family of relations between tautological cohomology classes of Mbar_{g,n}

**Abstract Kazarian:**

Double Hurwitz numbers enumerate possible ways to represent the identical permutation as the product of two permutations of given cyclic types and a given number of transpositions. In topological terms, they describe topologically distinct meromorphic functions on Riemann surfaces of given genus with prescribed critical values and prescribed orders of poles and zeroes. These numbers themselves are well studied and there are known formulas for their generating function. In spite of the existence of such formulas and a variety of modern proofs, many natural questions concerning these numbers remain open.

We propose a new recursion for these numbers that has a topological origin: it is derived from cohomological information contained in the stratification of the Hurwitz space by multisingularities of the functions. We expect that variations of this approach could be adopted to other families of Hurwitz numbers for which closed formulas are not known at the moment, including those for curves of higher genera.

(Joint work with S.Lando and D.Zvonkine)

**Abstract van de Leur:**

Milanov and Tseng conjectured that the total descendent potential of the orbifold C_{k;m} is a tau function of the extended bigraded Toda hierarchy. We prove this conjecture.

(Joined work with Guido Carlet)

**Abstract Zvonkine:**

Let M_g be the moduli space of smooth curves of genus g. As g tends to infinity, the cohomology ring of M_g stabilizes to Q[kappa_1, kappa_2, …] for certain natural cohomology classes kappa_m. For a fixed g, however, there are polynomial relations between the kappa-classes. The study of these relations was started by C. Faber in 1993 and is still not finished 20 years later.

We can complicate the problem by adding marked points and passing to the Deligne-Mumford compactification of the moduli space, which greatly increases the number of generators and relations. We will construct a family of relations between these generators that contains all known relations and, conjecturally, all existing relations. The construction involves r-spin structures (r-spin = r-th root of the cotangent line bundle to the curve) and Frobenius manifolds.

(Joint work with A. Pixton et R. Pandharipande)

The defence of Alexandr Buryak will take place on 10:00 at the Agnietenkapel (Oudezijds Voorburgwal 229-231, 1012 EZ Amsterdam). Title of the thesis: “Topology of the moduli space of curves and integrable hierarchies”.

Everybody is welcome!

**Operations on Hochschild complexes, revisited
**

**Speaker:** Boris Tsygan (Northwestern University)

**Date and time:** Thursday, March 28th, 2013 from 16:00-17:00hrs

**Location:** UVA, Science Park 904, Room A1.06

**Title:** Operations on Hochschild complexes, revisited.

**Abstract:** Algebraic structures on Hochschild cochain and chain complexes of algebras are long known to be of considerable interest. On the one hand, some of them arise as standard operations in homological algebra. On the other hand, for the ring of functions on a manifold, Hochschild homology, resp. cohomology, is isomorphic to the space of differential forms, resp. multivector fields, and many algebraic structures from classical calculus can be defined (in a highly nontrivial way) in a more general setting of an arbitrary algebra and its Hochschild complexes. Despite an extensive amount of work on the subject, it appears that large parts of the algebraic structure on the Hochschild complexes of algebras and their tensor products are still unknown. I will review the known results (Kontsevich-Soibelman, Dolgushev, Tamarkin and myself, Keller) and then outline some provisional results and conjectures about new operations. The talk will not assume any prior knowledge beyond basic facts about complexes and (co)homology.

**GQT colloquium Nijmegen
**

**place:** Radboud Universiteit Nijmegen, Huygensgebouw

**time:** 13:00 – 17:00

**room:** HG00.108

**program:**

13:00 – 14:00 **Christian Voigt **(University of Glasgow)

**The string group and vertex algebras **

The string group String(n) is an infinite dimensional analogue of the spin group Spin(n) familiar from geometry and index theory. In this talk I will discuss a tentative realisation of String(n) using unitary vertex superalgebras and field algebras. This includes a categorified analogue of the Clifford algebra and its spinor representation, and I will explain carefully the analogy to the situation for the spin group.

14:30 – 15:30 **Simon Salamon **(King’s College London)

**Surveying points in the complex projective plane **

I shall introduce Zauner’s conjecture on the existence of SIC-POVM’s (symmetric informationally complete positive operator valued measures, that correspond to n^2 equidistant points in CP^(n-1) with the Fubini-Study metric). The theory will be illustrated in only the simplest situations of n=3 and 4, but from a geometer’s perspective using the concept of moment mapping.

16:00 – 17:00 **Raf Bocklandt **(Universiteit van Amsterdam)

**Noncommutative mirror symmetry for punctured surfaces **

A dimer model on a surface with punctures is an oriented graph such that its nodes correspond to the punctures and the arrows circle round the faces they cut out. To any dimer model Q we can associate 2 categories: A wrapped Fukaya category F(Q) and a category of matrix factorizations M(Q).

In both categories the objects are arrows, which are interpreted as Lagrangian subvarieties in F(Q) and will give us certain matrix factorizations of a potential on the Jacobi algebra of the dimer in M(Q).

We show that there is a duality D on the set of all dimers such that for consistent dimers the category of matrix factorizations M(Q) is isomorphic to the Fukaya category of its dual, F(D(Q)). We also discuss the connection between classical mirror symmetry.

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**15.00:** Tea

**15.30-16.30:** Colloquium Lecture, Pangea Lecture Theater, Koningberger building

**16.30:** Drinks in the Library

Two more seminar lectures by Professor Madsen from **11.00-12.00** and **15.00-16.00** in the **Hans Freudenthal Building **, room 611

We would like to announce the ninth workshop of the series on “Higher Geometric Structures along the Lower Rhine”, jointly organized by geometers and topologists from Bonn, Nijmegen, and Utrecht.

The meeting will be held at Radboud University Nijmegen, on May 11-12, 2017.

The focus of this workshop series lies on the development and application of new structures in geometry and topology such as Lie groupoids, differentiable stacks, Lie algebroids, generalized complex geometry, topological quantum field theories, higher categories, homotopy algebraic structures, higher operads, derived categories, and related topics.

The speakers are:

Francesca Arici

Michael Bailey

Tyrone Crisp

Honglei Lang

Milena Pabiniak

Markus Pflaum

For the registration and more information please check site.

**Topology/geometry seminar: Ezra Getzler will give a talk on The derived Maurer-Cartan locus**

**Abstract:** This talk is based on a recent paper in l’Enseignement Mathématique of this title. There are two models for derived schemes: differential graded manifolds and cosimplicial manifolds. The cosimplicial formalism is more general: in this talk, I construct a functor from differential graded Lie algebras to cosimplicial manifolds which represents the derived Maurer-Cartan locus. The talk will be a very gentle introduction to this subject: some background in the theory of simplicial and cosimplicial abelian groups is useful but not required.

As always, all interested are welcome.

Ieke Moerdijk

**Workshop on generalized geometry
**

We are organizing a mini workshop on the occasion of Joey van der Leer Duran’s graduation. The meeting will take place in the Sonnenborgh Observatorium on the 30th of November. The speakers will be Gueo Grantcharov, Ioan Marcut and Brent Pym.

Registration is free and people attending the workshop will be provided with coffee and lunch. To help us with the planning, please register if you intend to come.

**GQT school and colloquium
**

Will take place in Ernst Sillem Hoeve Hotel and Conference Center form the 28th of November to the 2nd of December.

School lectures will be:

Martijn Kool — Toric varieties and equivariant vector bundles

Suijlekom & Arici — Noncommutative geometry and gauge theories

Gerard van der Geer — Modular forms

See the event webpage for registration and further details.

**Workshop: The Big Picture (on the occasion of Jan Stienstra’s retirement)
**

**Date:** Friday November 25, 2016 (10.30-17.30).

**Speakers:**

Raf Bocklandt (UvA)

Vasily Golyshev (Moscow)

Anton Mellit (Trieste)

Duco van Straten (Mainz)

**Registration:
**Participation in this symposium is open and free to all interested, but registration is required. Please register by sending an email to science.secr.mathins@uu.nl as soon as possible. Mention in this email “JS65”. Lunch (Yes or No; Also, if you have special dietary requirements, please let us know). For more information click on the link above.

**Mini-workshop on symplectic geometry
**

On September 30 we will organize a mini-workshop on symplectic geometry at the VU Amsterdam. It is aimed at researchers, Ph.D. students, and advanced master’s students working in symplectic geometry and related areas. The speakers are:

Hansjörg Geiges (Universität zu Köln)

Urs Frauenfelder (Universität Augsburg)

Alexander Ritter (University of Oxford)

Lev Buhovski (Tel Aviv University)

* If you are interested in participating then please register.

Please indicate if you will join us for dinner.

organizers:

Oliver Fabert (VU Amsterdam)

Fabian Ziltener (Universiteit Utrecht)

**GQT School and Colloquium
**

The next GQT school and colloquium will take place in Woudschoten Hotel and Conference Center form the 6th to 10th of June. School lectures will be:

Ioan Marcut — Dirac Structures

Gert Heckman — Complex reflexion groups

Nicolai Reshetikhin — BV-quantization

See the event webpage for registration and further details.

**2nd Kan memorial lectures
**

We are honoured that Graeme Segal (Oxford) will give the 2nd Kan Memorial Lectures at Utrecht University.

The lectures start with a colloquium style talk on 2 June, in the

**The Ubiquity of Homotopy, **15.30-16.30

Refreshments beforehand from 15.00-15.30

Drinks afterwards from 16.30-17.00 in the mathematics library

Two more specialised lectures will follow on

Friday 3 June, in The **Hans Freudenthal building, room 611**

**Aspects of non-commutative geometry, **11.00-12.00

**Higher structures in homotopy theory, **15.00-16.00

**Abstract**

Much of mathematics is about discovering robust kinds of structure which organize and illuminate large areas of the subject. Perhaps the most basic organizing concept of our thought is space. It leads us to the homotopy category, which captures many of our geometric intuitions but also arises unexpectedly in contexts far from ordinary spaces. Still more is this true of the `stable homotopy’ category, which sits midway between geometry and algebra.

The theme of my lectures is the strangeness and the ubiquity of the homotopy and stable homotopy categories, and how they give us new ideas of what a space is, and why manifolds and spaces with algebraic structure play such a special role. The first lecture will be a non-technical survey of things discussed in more detail in the following two, such as the dual ways of thinking of a space in terms of the paths in it and in terms of its algebra of functions; also, what abstract homotopy theory is, and how it leads us to new geometrical ideas and new analogues of the stable homotopy category.

One of the biggest steps in disengaging homotopy from spaces was Kan’s theory of simplicial objects; a subtheme is the different ways in which this can be viewed and the different directions in which it can lead.

The second lecture focuses on the relation between spaces and their algebras of functions, algebraic K-theory, and the nature of noncommutative spaces and `quantization’ – what it means for a noncommutative object to be a deformation of a normal space. We see how the stable homotopy category sits inside a noncommutative stable category. I shall speculate on the place of Floer homotopy theory in this picture.

The third lecture is partly about how manifolds relate to stable homotopy, and the role of Poincare duality and quadratic forms. It is also about the `higher homotopies’ which lie below the surface of the naive homotopy category. This is another angle on the interpolation between commutativity and noncommutativity, more from the perspective of traditional algebraic topology.

**Topics in the Langlands Correspondence**

Workshop on June 2nd and 3rd at the University of Amsterdam, Kortweg de Vries Institute on the occasion of the Ph.D. defense of Marcelo G. De Martino

**Location** SP 107, room F3.20

**Programme**

**Thursday 02/06**

**15:00-16:00:** Gordan Savin (University of Utah)

**16:15-17:15:** Erik van den Ban (Universiteit Utrecht)

**Friday 03/06**

**10:00-11:00:** Dipendra Prasad (Tata Inst. of Fund. Research)

**11:15-12:15:** Anne-Marie Aubert (Inst. Mathématiques de Jussieu)

Gordan Savin: TBA

Erik van den Ban: TBA

**Dipendra Prasad:** *A relative Local Langlands correspondence.*

**Abstract:** For E/F quadratic extension of local fields, we consider the question of classifying irreducible admissible representations of G(E) which carry a G(F)-inv. linear form. Although in a certain generic sense, one expects a simple answer – multiplicity 1, and exact characterization, the full answer is rather complicated – and interesting, involving geometry of Langlands parameters.

**Anne-Marie Aubert:** *Cuspidality and Hecke algebras for enhanced Langlands parameters*

**Abstract:** Enhanced Langlands parameters for a p-adic group G are pairs formed by a Langlands parameter for G and an irreducible character of a certain component group attached to the parameter. We will introduce a notion of cuspidality for these pairs, describe a construction of a cuspidal support map for enhanced Langlands parameters, and attach an almost affine Hecke algebra to every cuspidal support. It is joint work with Ahmed Moussaoui and Maarten Solleveld.

**Belgian-Dutch Algebraic Geometry Day
**

Friday April 22 in Leuven: 10th edition of the Belgian-Dutch Algebraic Geometry Days. Speakers: Sho Tanimoto (Copenhagen), John Christian Ottem (Oslo), Bruno Chiarellotto (Padova).

**Gauge Theory and Noncommutative Geometry
**

4-8 April 2016 at the Radboud University Nijmegen.

More details can be found **here**

If you’re interested in coming, please let us know by filling in the registration form.

**Organizing committee**

Simon Brain

Klaas Landsman

Walter van Suijlekom

**Mini-Workshop on Symplectic Geometry
**March 11th, 2016

This mini-workshop is aimed at researchers, Ph.D. students, and advanced master’s students working in symplectic geometry and related areas. It is organized jointly with the Vrije Universiteit Amsterdam.

This is the third workshop that we are organizing. These mini-workshops take place biannually. The goal is to strengthen the symplectic community of the Netherlands and to connect it with abroad. Topics include Hamiltonian dynamics, the symplectic embedding question, holomorphic curves, and Floer homology.

**Speakers**

Claude Viterbo (ENS Paris)

Janko Latschev (Universität Hamburg)

Yaron Ostrover (Tel Aviv University)

Chris Wendl (University College London)

**Organizers**

Oliver Fabert (Vrije Universiteit Amsterdam)

Fabian Ziltener (Universiteit Utrecht)

Please **register**by March 3!

For any question please contact Oliver Fabert at o.fabert@vu.nl and Fabian Ziltener at f.ziltener@uu.nl .

**Winter school: Banach methods in noncommutative geometry
**

From 25th-29th January, 2016 we have organized a winter school in Münster entitled *Banach methods in noncommutative geometry: isomorphism conjectures and geometry of groups.* The school is aimed at PhD students and postdocs as well as M.Sc. students continuing in academia. We will focus on the connection between Banach/operator space methods as approximation properties and geometric properties of groups and their connection to problems as the Baum-Connes and conjecture. We welcome young researchers in these, and neighbouring areas to participate.

**Lectures are given by:**

-Siegfried Echterhoff (Münster)

-Erik Guentner (Hawaii)

-Michael Puschnigg (Aix-Marseille)

-Mikael de la Salle (ENS Lyon)

-Guoliang Yu (Texas A&M)

Please register **here**

For information on funding we refer you to the website. The workshop has been organized together with the ANR SingStar project. Please feel free to forward the announcement to people who may be interested.

**Organizer:** Martijn Caspers, Maria-Paula Gomez, Pierre-Yves Le Gall, Walther Paravicini

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**13:45-14:30** Noud Aldenhoven (Radboud Universiteit) Explicit matrix inverses involving continuous q-ultraspherical polynomials and quantum groups

Coffee/tea

**15:00-15:45 **Tom Koornwinder (Universiteit van Amsterdam) Solutions of the system of pde’s voor Appell F_2 and their integral representations (partially following Olsson and Diekema)

**16:00-16:45** Mourad Ismail (University of Central Florida & King Saud University) Rogers-Ramanujan Identities

**Location:** HG00.310, Huygensgebouw, FNWI

Radboud Universiteit, Nijmegen

**Directions**

You are all cordially invited!

A dinner in downtown Nijmegen is planned, please email E. Koelink if you plan to join.

**Moduli spaces and Arithmetic Geometry: celebrating “FO80”
**

On Thursday, November 12, there will be a special afternoon to celebrate the 80th birthday of Frans Oort. There will be two lectures aimed at a broad audience of mathematicians. We are very honored to have

**Aise Johan de Jong (Columbia University, New York)** and **Don Zagier (MPI Bonn and ICTP Trieste)**

as speakers this afternoon. Everyone interested is cordially invited, but if you wish to attend, please register at

http://www.lorentzcenter.nl/lc/web/2015/810/pubinfo.php3?wsid=810&venue=De%20Sitter%20Lecture%20Room

The afternoon will be concluded with a reception.

The talks are given in the De Sitterzaal (ground floor Oort building, Niels Bohrweg 2, Leiden)

**Schedule:**

14:00 — 15:00 Aise Johan de Jong (title TBA)

15:00 — 15:30 coffee break

15:30 — 16:30 Don Zagier (title TBA)

16:30 — 18:00 reception in front of the De Sitterzaal

This special afternoon is part of the Lorentz workshop ‘Moduli spaces and Arithmetic Geometry’ that is held from 9 till 13 November.

Due to an overwhelming interest in this workshop, it is no longer possible to register as a participant, though it is possible to attend individual lectures.

**GQT graduate school and colloquium
**

**GQT School**

Stefan Behrens and Ralph Klaasse — Four-manifolds

Oliver Fabert — Floer theory

Erik Koelink — Quantum groups

**GQT colloquium**

Speakers for the colloquium include: Martijn Caspers, Kenny de Commer, Kim Froyshov, Peter Hochs, Vicky Hoskins

**Mini-Workshop on Symplectic Geometry
**

**Higher Geometric Structures along the Lower Rhine VI
**

Higher Geometric Structures along the Lower Rhine VI will take place in Van der Valk Hotel De Bilt/Utrecht on September 24-26.

**Speakers**

Matija Basic

Yael Fregier

Benoit Fresse

Vladimir Hinich

João Nuno Mestre

Steffen Sagave

Cornelia Vizman

Yannick Voglaire

Marco Zambon

**Student Seminar: Albebraic Geometry and Homotopy theory
**

**Workshop “Geometric Invariants and Spectral Curves”
**

On June 1-5 there is a workshop “Geometric Invariants and Spectral Curves” at the Lorentz Center, Leiden. Part of this workshop is specially targeted for PhD students. Everybody is welcome!

**Workshop on mathematical physics
**

On May 26-28 there is a workshop on mathematical physics at the University of Amsterdam. Everybody is welcome!

**Geometry Seminar
**

**Mini-Workshop on Symplectic Geometry, Universiteit Utrecht
**

This mini-workshop is aimed at researchers, Ph.D. students, and advanced master’s students working in symplectic geometry and related areas. It is organized jointly with the Vrije Universiteit Amsterdam.

This is the first instance of what we plan to make a biannual tradition. The goal of these mini-workshops is to strengthen the symplectic community of the Netherlands and to connect it with abroad. Topics will include Hamiltonian dynamics, the symplectic embedding question, holomorphic curves, and Floer homology.

**Speakers**

Kai Cieliebak (Universität Augsburg)

Felix Schlenk (Université de Neuchâtel)

Rob van der Vorst (Vrije Universiteit Amsterdam)

Frol Zapolski (University of Haifa)

**Organizers**

Oliver Fabert (Vrije Universiteit Amsterdam)

Fabian Ziltener (Universiteit Utrecht)

For any questions please contact Oliver Fabert at o.fabert “at” vu.nl and Fabian Ziltener at f.ziltener “at” uu.nl .

This mini-workshop is supported by the Universiteit Utrecht, the Vrije Universiteit Amsterdam, and the Geometry and Quantum Theory Cluster.

**Workshop on Algebraic Geometry
**

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3 – 5 Novmber 2014: GQT graduate school

6 – 7 November 2014: GQT Colloquium

location: NH Zandvoort, Zandvoort

website: GQT colloquium

The school will focus on three topics:

– Maarten Solleveld: p-adic groups (3 Nov)

– Jasper Stokman: Quantum integrable systems (4 Nov)

– Andre Henriques: K-theory (5 Nov)

The colloquium will consist of several talks related to the topics discussed during the school as well as some talks on general GQT themes. For details, visit the event’s webpage.

Both events are aimed primarily at GQT-members, with the school aiming especially at PhD-students.

**Integrability and Isomonodromy in Mathematical Physics
**

A workshop at the Lorentz Center. More information to follow.

**GQT Graduate School and Colloquium
**

30 June – 2 July 2014: GQT graduate school

3 – 4 July 2014: GQT Colloquium

location: Woudschouten conference center, near Zeist

website: http://www.projects.science.uu.nl/GQT/GQT_colloquium

The school will focus on three topics:

– Raf Bocklandt: Mirror symmetry

– Carel Faber: Gromov-Witten invariants in algebraic geometry

– Ben Moonen: Hodge structures

The colloquium will consist of several talks related to the topics discussed during the school as well as some talks on general GQT themes. The speakers are:

Chris Peters, Jozef Steenbrink, Barbara Fantechi, Tom Coates, Silvia Sabatini, Nathalie Wahl, Ed Segal, Mingmin Shen and Stefan Vandoren.

Both events are aimed primarily at GQT-members, with the school aiming especially at PhD-students.

**Higher Geometric Structures along the Lower Rhine V
**

This meeting will take place in Nijmegen from June 19-20, 2014**Speakers**

Larry Breen (Paris 13)

Yonatan Harpaz (Nijmegen)

Ralph Kaufmann (Purdue and MPIM)

Pascal Lambrechts (Louvain-la-Neuve)

Silvia Sabatini(Lisbon)

Urs Schreiber (Nijmegen)

Daniele Sepe (Utrecht)

Participation is free, but registration is necessary for the obvious logistic reasons. For further information, see

http://www.ru.nl/math/research/vmconferences/2014-higher/

**Workshop on Instanton Counting: Moduli Spaces, Representation Theory and Integrable Systems
**

Over the last 30 years there have been remarkable instances where physical theories provided a formidable input to mathematicians, off ering the stimulus to the creation of new mathematical theories, and supplying strong evidence for highly nontrivial theorems. An example of this kind of interaction between mathematics and physics is gauge theory, and, in particular, instanton counting. This refers to the study of the relevant partition functions (such as the Nekrasov partition functions) in gauge theory by using an algebro-geometric approach, and is related to some highly nontrivial mathematical problems (such as the Alday- Gaiotto-Tachikawa conjecture) which come from physical issues in gauge and conformal field theory.

This workshop aims at assessing the state of the art in this area of research in its various aspects. In particular, it focuses on various aspects of the geometry of the moduli spaces of framed sheaves and of Nakajima quiver varieties, of their relations to integrable systems, of the instanton counting on toric surfaces and of the AGT conjecture. We believe that a more fruitful interaction between the different communities of people working in these fields will strengthen them individually and collectively.

Invited speakers: Alexander Belavin, Mikhail Bershtein, Alexander Braverman, Erik Carlsson, Duiliu Emanuel Diaconescu, Michael Finkelberg, Evgeny Gorsky, Weiping Li, Hiraku Nakajima, Mattia Pedrini, Rubik Poghosyan, Giulia Sacc�, Justin Sawon, Richard J. Szabo, Alessandro Tanzini, Eric Vasserot, Niclas Wyllard

For more information and registration please go to the web-page of the Lorentz Center.

**Workshop “Knots and Physics”
**

On May 20-21, 2014, we have a workshop “Knots and Physics” on the occasion of the thesis defense of Alexey Sleptsov. The speakers are A. Brini, V. Dolotin, E. Gorsky, A. Mironov, A. Morozov, J. Rasmussen, A. Sleptsov, P. Sulkowski, and P. Zinn-Justin.

Everybody is welcome!

**IMAPP Colloquium Alain Connes, Radboud University Nijmegen
**

Title: ‘The spectral model of particle physics’ Time: 16:00 Place: Radboud University Nijmegen – Huygensgebouw HG00.304

**4th workshop Higher Geometric Structures along the Lower Rhine
**

Announcing the fourth workshop of the series “Higher Geometric Structures along the Lower Rhine”, jointly organized by the Geometry/Topology groups in Bonn, Nijmegen, and Utrecht. This meeting will be held at the Max Planck Institute for Mathematics in Bonn on February 13-14, 2014.

**Speakers**

Dimitri Ara (Nijmegen)

Michael Batanin (Macquarie University, Sydney/MPIM)

Pedro Frejlich (Utrecht)

Bas Janssens (Utrecht)

Martin Markl (Prague/MPIM)

Eckhard Meinrenken (University of Toronto)

Matan Prezma (Nijmegen)

For registration and more information please visit the website: http://www.mpim-bonn.mpg.de/node/5119\

**Conference: The geometry of special functions
**

A two-day conference in Nijmegen, 30–31 January 2014

**Speakers: **

Masaaki Yoshida (Kyushu University, Fukuoka)

Daniel Allcock (University of Texas, Austin)

Duco van Straten (Johannes Gutenberg Universität Mainz)

Michele Vergne (Institut de Mathématiques de Jussieu, Paris)

Michel Duflo (Institut de Mathématiques de Jussieu, Paris)

Jasper Stokman (Universiteit van Amsterdam and Radboud Universiteit Nijmegen)

Jan Stienstra (Universiteit Utrecht)

Frits Beukers (Universiteit Utrecht)

**Organisers: **

Eduard Looijenga, Eric Opdam and Maarten Solleveld

**Workshop “Moduli of curves and mathematical physics”
**

On the occasion of the thesis defense of Loek Spitz, a workshop takes place on Thursday, January 23, 2014 at the University of Amsterdam (Plantage Muidergracht 24, 1018 TV Amsterdam, N.B.: This is OLD LOCATION of the KdV Institute). The lecture room is P0.18.

The program is as follows:

14:00-15:00 Alessandro Chiodo (Paris): Applications of quantum theories of Landau-Ginzburg models

15:00-15:15 Break.

15:15-16:15 Dimitri Zvonkine (Paris): The Chern character of the Verlinde bundle

16:15-16:30 Break.

16:30-17:30 Motohico Mulase (Davis): Quantum curves for Hitchin fibrations

Abstract Chiodo: Landau-Ginzburg models are singularities of the form f:X->B arising for instance as mirror partners of several Fano manifolds. More precisely, we consider mirror symmetry as an identification of two local systems. The first local system is classical in algebraic geometry and encodes the cohomology of the fibres of f:X->B. The second local system embodies quantum periods of the Fano manifold and arises from Gromov-Witten theory. Fan-Jarvis-Ruan and Polishchuk-Vaintrob set up analogue quantum theories applying also to Landau-Ginzburg models and allow us to cast mirror symmetry in a global, more flexible, framework. In this way some well known obstacles in Gromov-Witten theory become more approachable. In particular we will illustrate “non-convexity” and “non-concavity”, which are some of the main outstanding obstacles preventing us from knowing Gromov-Witten invariants in many major examples such as the quintic threefold in higher genus. I will describe recent work by Jérémy Guéré proving a mirror theorem relating certain Landau-Ginzburg models without concavity.

Abstract Zvonkine: We give an explicit formula for the total Chern character of the Verlinde bundle over the moduli space of stable curves in terms of tautological classes. The Chern characters of the Verlinde bundles form a semi-simple CohFT, while their ranks, given by the Verlinde formula, form a semi-simple fusion algebra. According to the Teleman’s classification of semisimple CohFTs, there exists an element of Givental’s group that transforms the fusion algebra into the CohFT. We determine this element using the first Chern class of the Verlinde bundle on the space of smooth curves, and the projective flatness of the Hitchin connection.

(Joint with A. Marian, D. Oprea, R. Pandharipande, A. Pixton)

Abstract Mulase: The quantum curves for SL(2)-Hitchin fibrations were constructed in October 2013 in a joint paper with Olivia Dumitrescu. In this talk we discuss two most recent topics in this direction of research: one is the action of the monodromy group of the Hitchin fibration on the family of quantum curves, and the other is a generalization of the theory to parabolic Hitchin fibrations. This research is motivated by understanding the AGT correspondence from the point of view of quantum curves.

The talk is based on the on-going joint work with Dumitrescu and Laura Schaposnik.

The defence of Loek Spitz will take place on 10:00 the same day at the Agnietenkapel (Oudezijds Voorburgwal 229-231, 1012 EZ Amsterdam). Title of the thesis: “Hurwitz numbers, moduli of curves, topological recursion, Givental’s theory and their relations.”.

Everybody is welcome!

**GQT Graduate School and Colloquium
**

The first GQT Graduate School (14-16 Jan) and Colloquium (17-18 Jan) will take place at Woudschoten conference center in Zeist.

Tutorials during the school:

- Klaas Landsman: What is noncommutative geometry?
- Hessel Posthuma: What is index theory?
- Fabian Ziltener: What is Gromov-Witten theory?

Confirmed speakers for the colloquium: Peter Albers (Muenster); Alessandro Chiodo (Jussieu); Xin Li (Queen Mary); Richard Sharp (Warwick); more to follow.

For information on registration, schedule and more see the event’s webpage.

]]>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
**

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
**

**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|
**

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
**

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
**

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
**

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

**Abstracts:**

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
**

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”
**

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
**

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
**

Location: Linnaeus building (Heyendaalseweg 137), room LIN 3.

Schedule:

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
**

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.

**Program: **

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 (J.Stienstra@uu.nl and J.W.vandeLeur@uu.nl) before Thursday January 5.

**Abstracts**

**Jean Fasel
**

Let R be a commutative noetherian ring. A projective R-module P is said to be stably free if P⊕R

**Henning Haahr Andersen
**

Let G be a reductive algebraic group over a field k, e.g. G = GL

**Antoine Touzé
**

Let V be a representation of the algebraic group GL

characteristic, one can use the Frobenius isomorphism of x→x

**Workshop: Higher geometric structures along the Lower Rhine, MPIM Bonn
**

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)

Speakers:

**13:00‒14:00 Klaas Landsman**:*The mathematics of mass: from the Higgs boson to Schrödinger’s cat***14:30‒15:30 Jesper Grodal**:*Finite loop spaces***15:45‒16:45 Guido Carlet**:*WDVV equations and 2+1 integrable systems*

Contact: Tilman Bauer

**Abstracts
**

Since the Higgs boson has not been found (yet), the speaker is among many who take a critical look at the Higgs mechanism that underlies the generation of mass in the Standard Model of elementary particle physics. This leads to fascinating mathematical questions involving C*-algebras, ground states, symmetry (breaking), phase transitions, and, perhaps unexpectedly, the insight that the Higgs mechanism is predicated on a solution of the infamous measurement problem in quantum mechanics (which, in a world premiere, we will present).

**Jesper Grodal** (University of Copenhagen)

*Finite loop spaces*

Hilbert’s 5th problem, in its most basic form, asks if every compact topological group, which admits the structure of a smooth manifold, is a Lie group. In this form, it was answered affirmatively by von Neumann in 1929. If one takes a homotopical interpretation of the word “admits”, the question is more subtle, and one is led to the notion of a finite loop space. These turn out not quite to be Lie groups, but nevertheless posses a rich enough structure to admit a classification. My talk will outline this story, which starts with a 1941 paper of Hopf: Über die Topologie der Gruppen-Mannigfaltigkeiten und ihre Verallgemeinerungen” and ends close to the present.

**Guido Carlet** (University of Copenhagen):

*WDVV equations and 2+1 integrable systems*

Frobenius manifolds, originating as a geometrical formulation of WDVV equations of two-dimensional topological field theory, provide an important tool to study certain dispersionless integrable systems in 1+1 dimensions. Recently there has been some progress in the program of extending the Frobenius manifold techniques to the case of integrable systems with two spatial variables, the so-called 2+1 integrable hierarchies. In this case the associated Frobenius manifold is infinite-dimensional. We will recall some basic definitions and constructions in the theory of Frobenius manifolds and, considering the example of the 2D Toda hierarchy, we will show that they extend to the infinite-dimensional case, provided that we require some analytical properties of the Lax symbols.

November 14th, 2011 – **Lecture Jun Tomiyama: A proposal for non-commutative spectral synthesis **

Time: 13.00-14.00 hr, room 412 of the Snellius building (Niels Bohrweg 1, Leiden)

Abstract (pdf format)

**GQT Colloquium Utrecht
**

The colloquium starts in the afternoon at 13.15 and will be held in Buys Ballot Laboratorium room 001.

**Schedule**

13.15-14.15: Simone Gutt Symplectic Dirac operators and Mp^c structures

14.30-15.30: Ieke Moerdijk Infinity-Categories and Infinity-Operads

15.30-16.00: coffee and tea

16.00-17.00: Carel Faber Modular forms and the cohomology of moduli spaces

17.05-18.00: drinks

**Abstracts**

**Simone Gutt:** My talk will be based on some ongoing work with Michel Cahen and John Rawnsley. Symplectic spinors have been introduced by Kostant on symplectic manifolds admitting a metaplectic structure, (the metaplectic group being a double cover of the symplectic group, the analogue of the Spin group in Riemmannian geometry). In that context, K. and L. Habermann have introduced two natural Dirac operators, choosing a compatible almost complex structure and a linear connexion preserving the symplectic 2-form. The commutator of those operators is elliptic. We extend the construction of symplectic Dirac operators to any symplectic manifold through the use of Mp^c structures. The group Mp^c is the analogue of the Riemmannian Spin^c and is a circle extension of the symplectic group. Mp^c-structures exist on any symplectic manifold and equivalence classes are parametrized by elements in H^2(M,Z). For any Mp^c structure, choosing a compatible almost complex structures and a linear connection, there are two natural Dirac operators, acting on the sections of a spinor bundle, whose commutator is elliptic. Using the Fock description of the spinor space allows the definition of a notion of degree and the construction of a dense family of finite dimensional subbundles stabilized by this operator.

**Carel Faber:** This will be an overview over the cohomology classes on moduli spaces of curves or abelian varieties (of low genus respectively dimension) corresponding to modular forms. Elliptic cusp forms give classes for curves of genus 1, and their generalizations, Siegel cusp forms, give classes for abelian varieties. One obtains a formula for moduli of pointed curves of genus 2 in these terms. For curves of higher genus, Teichmüller modular forms enter the picture. The related cohomology classes are still quite mysterious. (Joint work with Jonas Bergström and Gerard van der Geer.)

**GQT colloquium Nijmegen
**

**Location**: RU Nijmegen, Linneausgebouw, LIN 5

**Schedule**:

10:45-11:15 – Coffee and Tea

11:15-12:15 – Yong-Geun Oh

12:15-13:45 – Lunch

13:45-14:45 – Alexander Braverman

14:45-15:00 – Announcements of the GQT board

15:00-15:30 – Coffee and tea

15:30-16:30 – Erik van den Ban

16:30-18:00 – Reception (in the Huygens building)

**Titles and abstracts:**

**Yong-Geun Oh (University of Wisconsin-Madison)**

*Counting embedded curves in Calabi-Yau threefolds and Gopakumar-Vafa invariants*

The Gopakumar-Vafa BPS invariant is an integer invariant of the cohomology of D-brane moduli spaces on Calabi-Yau threefolds in string theory. By a conjectured relationship to Gromov-Witten theory, it is expected that the invariant coincides with the “number” of embedded (pseudo-)holomorphic curves. In this talk, we will explain how the latter integer invariants can be defined for a generic choice of compatible almost complex structures. If time permits, we will comment on the corresponding analog to the open string case and some implications on the wall-crossing phenomenon and open questions towards complete solution to the Gopakumar-Vafa conjecture.

**Alexander Braverman (Brown University):**

*Instanton counting and geometric representation theory*

This talk will be a survey of known results about (equivariant) cohomology and K-theory of various moduli spaces closely related to the moduli space of principal G-bundles (here G is a simply connected semi-simple algebraic group over complex number) on the projective plane trivialized at infinity (this is also the same as the moduli space on “instantons on R^4 framed at infinity”). The purpose of the talk will be two-fold: 1) Explain more precisely what kind of moduli spaces we should be talking about and explain why physicists what to integrate various cohomology (or K-theory) classes over these moduli spaces and what kind of answers they expect to get (and why). 2) Explain how one can understand the cohomology (or K-theory) of the above moduli spaces by representation-theoretic means and how this helps to prove predictions from 1 (in some cases).

**Erik van den Ban (Utrecht):**

*Cusp forms on reductive symmetric spaces. (joint work with Job Kuit)*

For a real reductive Lie group G, there exists a notion of cusp form, introduced by Harish-Chandra, who used this terminology to emphasize the analogy with the general theory of automorphic forms. The cusp forms coincide precisely with the discrete part of the spectral decomposition of the space of square integrable functions on G. This is in contrast with the theory of automorphic forms, where the discrete part of the spectral decomposition is built from cusp forms and residues of Eisenstein series, which in turn are built from cusp forms of lower rank subgroups. The class of reductive symmetric spaces contains that of the real reductive groups. It would be interesting to have a notion of cusp forms in this setting too. However, the definition of cusp forms is somewhat problematic due to the divergence of certain integrals. A number of years ago, M. Flensted-Jensen suggested an idea for such a definition, but the convergence of cuspidal integrals remained an unsolved issue in general. In this talk, based on ongoing joint work with Job Kuit, I will discuss this convergence problem, and present the solution for symmetric spaces of split rank 1. It turns out that in general the discrete spectrum splits into a cuspidal and a residual part.

**EWM summer school
**

The European Women in Mathematics organise a summer school for PhD students.

**Special day on Lie groups
**

This workshop is organized at the occasion of the thesis defense of Job Kuit, the day before.

Lectures:

11:00 – 11:50, T. Kobayashi (Univ. of Tokyo): Restrictions of Verma modules to symmetric pairs and some applications to differential geometry

13:00 – 13:50, S. Helgason (MIT): TBA

14:10 – 15:00, H. Schlichtkrull (Univ of Copenhagen): Decay on homogeneous spaces of reductive type

**Thesis defense of Job Kuit
**

On Monday May 16, 14:30, Job Kuit will defend his thesis: “Radon transformation for reductive symmetric spaces: support theorems”.

**GQT Colloquium
**

Place: Minnaert building room 211, de Uithof, Utrecht.

10.45 – 11.15 Coffee & tea

11.15 – 12.15 **Gerard van der Geer** Modular forms for genus three

12.15 – 14.00 Lunch

14.00 – 15.00 **Ulrike Tillmann **Cobordism theory: old and new

15.00 – 15.30 Coffee & tea

15.30 – 16.30 **Arno Kuijlaars **Multiple orthogonal polynomials and random matrix eigenvalues

16.30 – Drinks in Library Math. building

**Abstract **

**Ulrike Tillmann **

With the work of Thom in the early 1950s cobordism theory became an important tool for the classification of smooth manifolds. Cobordisms played a very different role in the axiomatic approach to topological quantum field theory by Atiyah and Segal in the late 1980s. In this lecture I will bring these two themes together and explain how recent results shed new light on both of these.

**Arno Kuijlaars**

The Gaussian Unitary Ensemble is the simplest unitary invariant random matrix ensemble. Its eigenvalues can be analyzed in full detail with the use of Hermite polynomials. General unitary ensembles are associated with orthogonal polynomials with exponential weights. In the fundamental work of Deift et al. (1999) the steepest descent analysis of the Riemann-Hilbert problem for these polynomials was developed in order to establish universality for eigenvalue spacings. Multiple orthogonal polynomials play a similar role in certain other random matrix ensembles such as the random matrix model with external source, and the two-matrix model. I will discuss the Riemann-Hilbert problem and a vector equilibrium problem that describes the global distribution of eigenvalues and is crucial for the asymptotic analysis.

**Inaugural Lecture Nicolai Reshetikhin
**

Title: The harmony of Mathematics and Physics

Date/Time: Friday, February 18, 2011, 16:00

Location: Aula of the University of Amsterdam, Singel 411

**GQT Colloquium
**

The GQT Colloquium on Friday, February 18, 2011, will be combined with the inaugural lecture of Nicolai Reshetikhin.

**Venue:** Zaal AB.44, gebouw A, Roetersstraat 15, 1018 WB Amsterdam.

**Schedule:**

10:50-11:15 Coffee and tea

11:15-12:15 Talk Marc Levine

12:15-13:45 Lunch break

13:45-14:45 Talk Michel van den Bergh

After the last lecture everybody is invited to attend the inaugural lecture of Nicolai Reshetikhin, See “The harmony of Mathematics and Physics”.

**Abstracts**

**Mark Levine**

*Some applications of algebraic cobordism*

Abstract: Algebraic cobordism is a version in algebraic geometry of the topological theory of complex cobordism. Originally, it was constructed to help understand rather subtle divisibility properties of characteristic classes, which in turn leads to some interesting results on homogeneous varieties over non-algebraically closed field. Later on, Pandharipande saw how to apply this theory to solve problems in Donaldson-Thomas theory. I will describe the theory of algebraic cobordism and say a bit about its original series of applications to homogeneous varieties, then turn to the work on Donaldson-Thomas theory and conclude with some more recent work of Pandharipande, Lee and Tzeng using algebraic cobordism to study problems in Gromow-Witten theory.

**Michel van den Bergh
**

Abstract: Kontsevich’s celebrated formality theorem shows that every Poisson bracket on a C^infty manifold can be quantized into a start product. For a smooth algebraic variety this is not quite true. We will discuss the algebraic version of the formality theorem and its relation to deformation theory. We will also discuss how algebraic formality may be used to prove a conjecture by Caldararu which gives an intriguing connection between algebraic geometry and Lie theory.

**Date:** Monday 20 December

**Place:** room 611, Mathematics Building, Utrecht

**Schedule:**

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
**

**Speakers**

**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.

**Program**

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).

**Schedule**

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
**

**Place**: Minnaertbuilding room 023, de Uithof, Utrecht

**Program**:

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

(drinks)

If you want to attend, please send an e-mail to: J.W.vandeLeur@uu.nl

**Promotie Bas Janssens
**

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.
**

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

More details: see conference website

**G. Felder lectures
**

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

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:

Thursday June 24 in HG00.071 of the Huygens Building:

**GQT colloquium Utrecht
**

**Place:** Minnaert building room 208, Utrecht

**Schedule**

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

**Abstracts.**

**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
**

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”
**

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 masterclassmph@gmail.com

**Talk by Pablo Roman (KU Leuven) in Mathematical Physics Seminar.
**

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
**

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)
**

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
**

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
**

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
**

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
**

**Location**

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

**Schedule**

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

**Abstracts**

**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
**

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.

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