© Gaëtan Borot

Noncommutative geometry meets topological recursion

16-20 August 2021, Münster, Germany

This workshop intends to be a first meeting point for specialists and young researchers active in noncommutative geometry, free probability, and topological recursion. In the two first areas, one often wants to compute expectation values of a large class of noncommutative observables in random ensembles of (several) matrices of size N, in the large N limit. The motivations come from the study of various models of 2d quantum gravity via random spectral triples, or from the problem of identifying interesting factors via approximations by matrix models. Topological recursion and its generalisations provide a priori universal recipes to make and to compactly organise such computations, not only for the leading order in N, but also to all orders of expansion in 1/N. In this way connections are established to domains like enumerative geometry, tropical geometry, mirror symmetry, topological and more generally low-dimensional quantum field theories where topological recursion has also been applied.

Concretely, the last 10 years have witnessed the developement

  • of analytic techniques to establish the existence of large-N asymptotic expansions,
  • of applications of the topological recursion to a growing class of matrix models which now include some of direct interest in the study of random spectral triples and in noncommutative probability,
  • and of connections between the combinatorics of free probability (i.e. higher order free cumulants) and the topological recursion together with symplectic transformations acting on it.

The workshop will explore the consequences of these remarkable algebraic structures axiomatised in topological recursion for problems in noncommutative geometry and free probability. Knowledge will also flow in the other direction, as the very nature of topological recursion hints at connections to (noncommutative) algebraic geometry and to Hopf algebraic structures and Connes-Kreimer renormalisation.

Mathematical models and phenomena under consideration are common to all these fields, and we wish to unite the strength of probabilistic/asymptotic, algebraic/geometric and combinatorial approaches for the benefit of all the communities involved. This interaction should in fine lead to a better geometric understanding, more powerful computational tools, and new results.

Minicourses

Introduction to topological recursion

Elba Garcia-Failde (IRIF, Université Paris Diderot)

Noncommutative geometry and spectral triples

Walter van Suijlekom (IMAPP, Radboud University Nijmegen)

Free probability and higher order freeness

Roland Speicher (Fachrichtung Mathematik, Universität des Saarlandes)

(Mixed) topological recursion and the two-matrix model

Bertrand Eynard (Institut de Physique Théorique, Paris-Saclay / IHÉS)

Organisers

Gaëtan Borot (Institut für Mathematik & Institut für Physik, Humboldt-Universität zu Berlin)

Masoud Khalkhali (Department of Mathematics, University of Western Ontario)

Hannah Markwig (Fachbereich Mathematik, Eberhard Karls Universität Tübingen)

Jörg Schürmann (Mathematisches Institut, WWU Münster)

Raimar Wulkenhaar (Mathematisches Institut, WWU Münster)

Preliminary list of participants

Alexander Alexandrov (Pohang), Francesca Arici (Leiden), Shahab Azarfar (Toronto), Marco Bertola (Montréal), Valentin Bonzom (Paris), Gaëtan Borot (Berlin), Johannes Branahl (Münster), Erwan Brugalle (Nantes), Renzo Cavalieri (Colorado), Severin Charbonnier* (Bonn), Remi Avohou Cocou (Bonn), Benoît Collins (Kyoto), Rui Dong (Nijmegen), Bertrand Eynard (Saclay/IHÉS), Elba Garcia-Failde (Paris), Alessandro Giacchetto (Bonn), Lisa Glaser (Wien), Harald Grosse (Wien), Marvin Anas Hahn (Frankfurt), Alexander Hock (Münster), Roberta Anna Iseppi (Aarhus), Masoud Khalkhali (London, ON), Dirk Kreimer (Berlin), Hélder Larraguivel (Warszawa), Danilo Lewanski (IHÉS), Camille Male (Bordeaux), Hannah Markwig (Tübingen), Grigori Mikhalkin (Genève), James Mingo (Kingston), Jonathan Novak (San Diego), Nicolas Orantin (Genève), Erik Panzer (Oxford), Frédéric Patras (Nice), Carlos Pérez Sánchez (Warszawa), Kasia Rejzner (York), Dimitri Shlyakhtenko (Los Angeles), Jörg Schürmann (Münster), Sergey Shadrin (Amsterdam), Piotr Śniady (Warszawa), Yan Soibelman* (Kansas), Roland Speicher (Saarbrücken), Piotr Sułkowski* (Warszawa), Ran Tessler (Weizmann Inst), Bruno Vallette (Paris), Walter van Suijlekom (Nijmegen), Zhituo Wang (Harbin), Raimar Wulkenhaar (Münster), Karen Yeats (Waterloo)

*to be confirmed

Schedule

to be announced

Registration

to be announced

Support and child care

Child care is available free of charge for all participants of the workshop.

Venue and Travel Information

The conference takes place in room SRZ 217 on the second floor of the seminar building located at

Orléans-Ring 12
48149 Münster
Germany

Google Maps

The University of Münster is located in Münster in Westphalia. The address of the Faculty of Mathematics and Computer Science is Einsteinstrasse 62 and is listed on all common route planners.

You can find the Cluster of Excellence Mathematics Münster in the annex:

Orléans-Ring 10
ground floor
48149 Münster

The conferences and workshops take place at the:

Seminar room center (SRZ)
Orléans-Ring 12
2nd floor
48149 Münster

Directions can be found on openstreetmap or on the Campus map of the University of Münster.

Detailed travel information can be found on the MM websites.

Download: Information for conference guests / Informationsblatt für TagungsteilnehmerInnen [de|en]

Poster

Once available, you are welcome to download the poster of the conference and display it in your institution.

Sponsors

The conference is supported by the Cluster of Excellence Mathematics Münster, the CRC Geometry: Deformations and Rigidity and the Humboldt University Berlin.