Holonomic generating functions and groups

Date: Thursday 21 July 2022

Abstract

A recurring theme in group theory is to understand the asymptotics and structure of groups with the use of generating functions that have nice descriptions and closed forms. For example, it is well known that the volume growth series of every hyperbolic/Coxeter group is rational, that is, it can be written as a fraction of two polynomials; and that the cogrowth (i.e., the growth of the word problem) for a hyperbolic group is algebraic (i.e., is a solution to a polynomial equation).

In this talk, we are interested in (multivariable) generating functions coming from groups that can be described using the more general framework of holonomic functions. In particular, we cover several cases where this class of functions arrives naturally. During this talk, we cover some lesser-known techniques and computational models from which holonomic power series arise.

This seminar wil be held in a hybrid format, with a face-to-face seminar that will be live streamed.