Noncommutative Geometry Meets Topological Recursion (24w5502)

This workshop intends meeting point for specialists and young researchers active at the interface of non-commutative geometry, free probability, integrability and enumerative and tropical geometry, random matrices and topological recursion.

The last 10 years have witnessed the developement of analytic techniques to establish the existence of large N asymptotic expansions, of applications of Chekhov-Eynard-Orantin 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 non-commutative 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. There has also been tremendous progress in the study of Hurwitz numbers and in the use of integrable techniques in enumerative geometry and random matrices. These topics can be put in a broader context of mirror symmetry (correspondence between A-model and B-model), low-dimensional quantum field theories, the study of the spectra of large random matrices and operator algebras associated to them.

Following up on three earlier workshops of this kind (Münster 2021, Western Ontario 2022, ESI Vienna 2023), with this workshop we wish to continue encouraging discussions and exchange of ideas and techniques between reseachers working in these topics understood in a very broad sense. In all the themes mentioned one finds common algebraic structures, a similar relevance of analytic techniques and the appearance (if not already in the very problems under consideration) of combinatorial and geometric questions. The workshop should contribute to the longer-term goal of unifying of the strengths of probabilistic/asymptotic, algebraic/geometric and combinatorial approaches for the benefit of all the communities involved. One expects that it should in fine lead to a better geometric understanding, more powerful computational tools, and new results.

The program consists of research talks completed by 4 longer introductory lectures: on free probability (Marwa Banna), B-model (Si Li), integrability and matrix models (Di Yang), tropical enumeration (Hannah Markwig). Young researchers will also be given the opportunity to talk about their work.

The Institute for Advanced Study in Mathematics (IASM) in Hangzhou, China, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, are collaborative Canada-US-Mexico ventures that provide an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station in Banff is supported by Canada’s Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta’s Advanced Education and Technology, and Mexico’s Consejo Nacional de Ciencia y Tecnología (CONACYT).