Lecturer: Anton Nazarov (Visiting Professor, Saint Petersburg University)
Weekday: Wed, Fri
Time: 09:50-12:15
Venue: A3-1-301
Zoom: 204 323 0165
Password: BIMSA
Prerequisite
Representation theory of symmetric group, Lie groups and Lie algebras, random matrix theory. Acquaintance with the material from the my previous courses "Asymptotic representation theory and random matrices", "From free fermions to limit shapes and beyond", courses of Pavel Nikitin "Asymptotic representation theory and random matrices", "Symmetric functions and representation theory", "Asymptotic representation theory" and course of Fan Yang "Topics in Random matrix theory" would be a plus, but is not required.
Introduction
A. Okounkov in the celebrated paper [1] has established the common limit of the mixed moments of random Young diagrams with respect to Plancherel measure and of random matrices from Gaussian Unitary Ensemble. He used the fact that moments of random matrices enumerate the maps of topological surfaces while representation theory of symmetric groups that produces Plancherel measure is connected to the description of essentially the same surfaces as the ramified coverings of the sphere.
In this course we will study this construction. Then we will discuss its possible extensions to other classical ensembles of random matrices, such as Laguerre and Jacobi Unitary Ensembles. Their counterparts in representation theory side of the correspondence are connected to Schur-Weyl duality and skew Howe duality.
This course extends the results covered in my minicourse "Random matrices and asymptotic representation theory" from January 2024, and has some overlaps with the lectures by Pavel Nikitin "Asymptotic representation theory and random matrices", but uses geometric approach. The lectures will be self-contained.
This course will be taught from June 20 to July 11, and from Aug. 20 to Sept. 3, 2025.
Lecturer Intro
Anton Nazarov is an associate professor at Saint Petersburg State University, Russia. He completed his PhD at the department of high-energy and elementary particle physics of Saint Petersburg State University in 2012 under the supervision of Vladimir Lyakhovsky. In 2013-2014 he was a postdoc at the University of Chicago. Anton's research interests are representation theory of Lie algebras, conformal field theory, integrable systems, determinantal point processes.
