Jonathan Novak (UC Sand Diego)

Department Colloquium

Speaker: Jonathan Novak (UC Sand Diego)

Title: Hypergeometric Functions of Many Variables

Abstract:
Many of the most widely used special functions in mathematics, science, and engineering are hypergeometric functions. This makes the question of several variables a natural one, and a number of distinct constructions of multivariate hypergeometric functions have been proposed. I will focus on hypergeometric functions of matrix arguments, which first arose in multivariate statistics some sixty years ago. In those halcyon days, population size was an arbitrary but fixed parameter. Today, in the age of big data, statisticians need to approximate hypergeometric functions of huge matrices. I will discuss an emerging approach to this high-dimensional problem based on techniques from algebraic combinatorics and enumerative geometry. I will explain how this approach completely solves an average case of the high-dimensional approximation problem in terms of certain (univariate) special functions from number theory, namely quasimodular forms.