After two earlier meetings with a similar theme in Muenster and London, Ontario, we are pleased to announce the third meeting to take place at Erwin Schroedinger Institute in Vienna in late April 2023.

# Noncommutative Geometry

## Sunday, March 26, 2023

## Saturday, February 25, 2023

### MPI Homage

The Max Planck Institute held this week a special event that officially closed down Manin's Seminar, after its continued existence since 1969, first in Moscow and then in Bonn. The event hosted a brief overview by Misha Kapranov on the history of the seminar, followed by two lectures, one by Don Zagier and one by myself. The videos of the lectures are available at this link:

Seminar on Algebra, Geometry and Physics: A Homage

https://archive.mpim-bonn.mpg.de/id/eprint/4867/

## Tuesday, January 10, 2023

### Мир без тебя

Юрий Иванович Манин (1937-2023)

https://listeningtogolem.blogspot.com/2023/01/blog-post.html

## Wednesday, May 18, 2022

### Hybrid Workshop on Noncommutative Geometry, Free Probability Theory and Random Matrix Theory, June 13 - 17, 2022, University of Western Ontario

This hybrid workshop is supported by the Fields Institute. All talks will be broadcast online. To gain access to the talks, please register free of charge here.

Workshop description: Topological recursion is a method for counting maps of a certain topology using only planar maps. The theory arose from work in 2D quantum gravity and the discovery that matrix integrals are related to maps on surfaces. These matrix integrals also appear in models of quantum gravity on noncommutative spaces and in quantum field theories on these spaces. The same matrix integrals arise in free probability and recent work has shown a surprising connection between higher order free independence and maps on surfaces of positive genus.

This workshop will bring together a group of researchers working in noncommutative geometry (NCG), free probability theory (FPT) and random matrix theory (RMT) to foster collaboration in an emerging area of research that is at the intersection of these three fields.

Mini courses

- Gaetan Borot (Humboldt University, Berlin): Asymptotics of matrix integrals and topological recursion.

- James Mingo (Queens, Canada): Free independence of random variables

- Raimar Wulkenhaar (Muenster, Germany): How topological recursion organises quantum fields on noncommutative geometries

This conference will be in hybrid format. All talks will be broadcast on zoom. To access the talks please register free of charge using the link provided above.

## Wednesday, September 1, 2021

### Global noncommutative geometry seminar (Americas) resumes this Friday, Sept 3, with a talk by Alain Connes

After a very successful first year, Global Noncommutative Geometry Seminar (Americas) starts again this Friday at 3 PM (Toronto time), 9 PM (Paris time) with a talk by Alain Connes. Title: On the Notion of Space.

Here is the Zoom link: Join Zoom Meeting

Passcode: 446996

Added Sept 7: Talk can be watched here

For abstracts and details of other forthcoming talks in Global Noncommutative Geometry Seminar please check the seminar website: Global NCG Seminar

## Sunday, August 22, 2021

### Online International Conference: Cyclic Cohomology at 40: achievements and future prospects

The year 2021 will mark the 40th anniversary of the discovery and development of Cyclic Cohomology Theory by Alain Connes. Its further flourishing fostered by many mathematicians including Dan Quillen, Jean Louis Loday, Boris Tsygan, Boris Feigin, Joachim Cuntz, Ib Madsen, Max Karoubi, and many others has brought a remarkable development of the subject in many distinct directions, in particular in global analysis, representation theory and index theory, algebraic K-theory and cyclotomic trace maps, arithmetic geometry and mathematical physics. The goal of this meeting will be to bring top experts from around the world to lecture on the state of the art in the field, to look towards the future and discuss the most pressing current open problems in the field.

For Conference Poster Click Here

Registration is free. To register please visit the Fields Institute Conference Page

## 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

*I**ntroduction to topological recursion*

*Elba Garcia-Failde (I**RIF, 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 *