June Huh - Volume Polynomials

Volume polynomials constitute a distinguished class of log-concave polynomials with remarkable analytic and combinatorial properties arising from convex bodies and projective varieties. I will introduce new entropy inequalities satisfied by volume polynomials, discuss applications to the combinatorics of algebraic matroids, introduce the new class of analytic matroids, and pose several open questions. (Based on various joint works with Lukas Grund, Mateusz Michalek, Henrik Süss, Botong Wang, and Jian Xiao).