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 

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

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

3. 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.  

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

https://wustl.zoom.us/j/95154904208?pwd=ajA2azAxK1ZwMlJUeXBEWlh5UG5WQT09

Meeting ID: 951 5490 4208

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

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

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

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

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

https://www.amazon.com/SHELL-BEACH-search-final-theory-ebook/dp/B08SM9B82P/ref=sr_1_1?dchild=1&keywords=shell+beach+grimstrup+jesper&qid=1612088711&sr=8-1

Fields Academy Graduate Courses

 Starting in January 2021, the Fields Institute in Toronto is going to run various advanced graduate courses in collaboration with Ontario universities. Students from all over the world can either take these courses, or just audit them. For details  see  here

                                                         

The Fields Academy has an undergraduate training component as well. For details  check