Abstract (Larry Rolen)

Abstract: The study of asymptotic properties of sequences is of
fundamental interest in number theory and combinatorics. We are
especially interested in proving inequalities among sequences of
numbers. This topic has seen a large outpouring of work in recent
years. For instance, Nicolas and DeSalvo–Pak independently proved that
the partition function $p(n)$ is eventually log-concave. Specifically,
they showed that $p^{^2}(n)-p(n-1)p(n+1)\geq0$ for $n\geq 26$. Work of
Griffin, Ono, Zagier, and myself placed this in a larger context by
proving that related polynomial zero properties follow from a general
phenomenon dictated by Hermite polynomials. In this talk, describing
joint work with Koustav Banerjee and Kathrin Bringmann, I will present
a unified framework to prove a wide class of inequalities of
sequences.