TALK: Cynthia Vinzant
Thursday, November 01, 2018 at 2:00pm
2-361 Seminar Room
Title: Completely log-concave polynomials in theory and applications
Speaker: Cynthia Vinzant (North Carolina State University)
Abstract: Stability is a multivariate generalization for real-rootedness in univariate polynomials. Within the past ten years, the theory of stable polynomials has contributed to breakthroughs in combinatorics, convex optimization, and operator theory. I will introduce a generalization of stability, called complete log-concavity, that satisfies many of the same desirable properties. These polynomials were inspired by recent work of Adiprasito, Huh, and Katz on combinatorial Hodge theory, but can be defined and understood in elementary terms. I will discuss the beautiful geometry underlying these polynomials and discuss some applications to negative dependence and counting problems in matroid theory. This is based on joint work with Nima Anari, Kuikui Liu, and Shayan Oveis Gharan.
Bio: Cynthia Vinzant is an assistant professor in the math department at North Carolina State University. Her research involves real algebraic geometry and connections with optimization, combinatorics, and computer science.