Cynthia Vinzant - Log Concave Polynomials and Matroids

Explore the fascinating world of log concave polynomials and matroids in this 58-minute lecture by Cynthia Vinzant at the Hausdorff Center for Mathematics. Delve into the functional properties of real multivariate polynomials and their applications in conic programming. Discover recent developments in matroid theory, including the strong log concavity of basis-generating polynomials and their implications for independence complex face numbers and random walk mixing times. Examine the connection between tropicalizations of these polynomials and M-concave functions. Learn about the combinatorial and geometric structures underlying this class of polynomials and their recent applications. The lecture covers topics such as multivariable calculus, logconcave coefficients, Markov chains, high-dimensional expanders, and polytope blind techniques, providing a comprehensive overview of this cutting-edge research area.

Introduction
Multivariable calculus
Logconcave coefficients
Proof of logconcave
Markov chains
Highdimensional expanders
Polytope blind
Summary