Joshua Swanson, USC  

Title: Cyclotomic generating functions

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. These and related polynomials have been studied for many years by a variety of authors from the fields of combinatorics, representation theory, probability, number theory, and commutative algebra. We call such polynomials *cyclotomic generating functions* (CGFs). We will review some of the many known examples and give results to classify the asymptotic behavior of their coefficient sequences in certain regimes. Joint work with Sara Billey.