CANCELLED Sara Billey: Cyclotomic Generating Functions

Location

FR4 (Oskar Klein), Albanova (directions available here ).

Schedule

14:15–15:00 Pre-colloquium by (TBA) in FD41.

15:15–15:30 SMC prizes for the academic year 2022/2023 will be announced and awarded.
15:30–16:30 Colloquium lecture by Sara Billey.
16:30–17:00 SMC social get together with refreshments.

Abstract

It is a remarkable fact that for many statistics on finite sets of combinatorial objects, the roots of the corresponding generating function are each either a complex root of unity or zero. We call such polynomials cyclotomic generating functions (CGF's) because of their close connections with the cyclotomic polynomials.

In this talk, we will review some of the many known examples of CGF's; describe their coefficients, moments, cumulants, and characteristic functions; and give a variety of necessary and sufficient conditions for their existence arising from probability, commutative algebra, and invariant theory.

Two important applications come from tableau and forest combinatorics following work of Björner and Wachs. We have also studied the family of CGF's from algebraic, analytic, and asymptotic perspectives. Many open problems concerning CGF's remain.

While the math in this talk has deep connections to many areas, we will emphasize the more accessible parts.