Tuesday, June 1, 2021

Noncommutative Geometry meets Topological Recursion (registration now open)





We plan to run the workshop in hybrid form with a considerable number of participants present in Münster and video transmission to the outside world.

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)

For Registration please check the 

Conference Website

Tuesday, May 25, 2021

Summer school on K-Theory and Representation Theory

 

An online summer school on K-Theory and Representation Theory, organized by N. Higson, R. Plymen and H. Sengun and sponsored by the London Mathematical Society and the Isaac Newton Institute, will take place 19-23 July 2021.

There will be four lecture series:

– Basic representation theory of p-adic Lie groups, by Anne-Marie Aubert

– Basic representation theory of real Lie groups, by Peter Hochs

– Basics of group C*-algebras and K-theory, by Bram Mesland

– Dirac operators and representation theory, by Hang Wang

The lectures will be aimed towards graduate students, but all are welcome to attend. Registration and further information are at https://sites.google.com/view/bath-21-dirac-induction/home

Sunday, February 21, 2021

SHELL BEACH - the search for the final theory, (guest post by Jesper Grimstrup)

My book SHELL BEACH - the search for the final theory is now out. In the book, which is written for a general audience, I discuss topics such as noncommutative geometry, loop quantum gravity and the question of a final theory - mixed with a dose of whitewater kayaking and massive (intellectual) waterfalls

Best wishes, Jesper Grimstrup