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This lecture from the 2025 Program for Women+ and Mathematics explores the theory of matroids and their connection to log-concave multivariate polynomials. Discover how matroids serve as combinatorial structures modeling independence in contexts like graph edges and vector spaces. Learn about the significance of log-concavity across mathematics, including combinatorics, algebraic geometry, convex analysis, and optimization. Examine the real and combinatorial geometry underlying log-concavity and its applications to matroids and random walk mixing times. Presented by Tracy Chin from the University of Washington at the Institute for Advanced Study, this 69-minute session is part of the Terng Lecture Course series scheduled for May 23, 2025, at 9:30am in Simonyi Hall 101.
