Welcome to the Rutgers Symmetric Functions & Probability Theory seminar page.
This seminar runs at 12:10 PM on Tuesdays in Hill 705.
The organizers are Swee Hong Chan , Konstantin Matveev, Siddhartha Sahi and Hong Chen.
This page is currently maintained by Hong Chen. If you wish to join our mailing list, please click here or email hc813@math.rutgers.edu.
For past talks, click here.
Speaker: Roger Van Peski (Columbia)
Title: Macdonald processes and universal limits in discrete random matrix theory
Abstract: Random matrices over the integers, finite fields, and p-adic integers have been studied since the late 1980s as natural models for random groups appearing in number theory and combinatorics. I will discuss some exact results relating them to Hall-Littlewood processes, explain their parallels with classical real/complex random matrix theory, and give probabilistic results on local limits which are the most difficult application of these tools. The latter results find a new limit process, the reflecting Poisson sea, which is a discrete-space local interacting particle system and appears as a universal limit of Hall-Littlewood processes.
Speaker: Hong Chen (Rutgers)
Title: Hypergeometric series associated with Jack and Macdonald polynomials (PhD Dissertation Defense)
Speaker: Songhao Zhu (Georgia Tech)
Title: Super Multivariate Krawtchouk Polynomials via Lie Superalgebras
Abstract: Krawtchouk polynomials constitute a family of orthogonal polynomials with applications in probability theory. In 2012, Iliev gave a Lie-theoretic interpretation of the multivariate Krawtchouk polynomials using certain representations of the Lie algebra $\mathfrak{sl}_n$. In this talk, we will present a superization of this interpretation, introduce super Krawtchouk polynomials with anticommuting variables, and explore their connection with zonal spherical functions on oriented Grassmannians. This is a joint work in progress with Plamen Iliev.
Speaker: Roger Van Peski (Columbia)
Title: Macdonald processes and universal limits in discrete random matrix theory
Abstract: Random matrices over the integers, finite fields, and p-adic integers have been studied since the late 1980s as natural models for random groups appearing in number theory and combinatorics. I will discuss some exact results relating them to Hall-Littlewood processes, explain their parallels with classical real/complex random matrix theory, and give probabilistic results on local limits which are the most difficult application of these tools. The latter results find a new limit process, the reflecting Poisson sea, which is a discrete-space local interacting particle system and appears as a universal limit of Hall-Littlewood processes.