Title: Cyclotomic generating functions
| Speaker: | Joshua Swanson |
| Affiliation: | University of Southern California |
| Location: | MC 5479 |
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.
There will be a pre-seminar presenting relevant background at the beginning graduate level starting at 1pm.