2025 Program for Women+ and Mathematics

Abstract: Matroids are combinatorial structures that model independence, such as that of edges in a graph and vectors in a linear space. I will introduce the theory of matroids along with their surprising connection to a class of multivariate polynomials that are log-concave on the positive orthant. Log-concavity is an important feature of many functions and discrete sequences appearing across mathematics, including combinatorics, algebraic geometry, convex analysis, and optimization. We will explore the real and combinatorial geometry underlying log-concavity along with applications to matroids and the mixing times of random walks.