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This lecture is the second part of the Terng Lecture Course on "Log-concavity and Matroids" presented by Josephine Yu from Georgia Institute of Technology as part of the 2025 Program for Women+ and Mathematics at the Institute for Advanced Study. Explore the fascinating theory of matroids, which are combinatorial structures modeling independence in contexts like graph edges and vector spaces. Discover the surprising connections between matroids and multivariate polynomials that exhibit log-concavity in the positive orthant. Learn about the significance of log-concavity across various mathematical fields including combinatorics, algebraic geometry, convex analysis, and optimization. Delve into the real and combinatorial geometry that underlies log-concavity and examine its applications to matroids and the mixing times of random walks in this comprehensive one-hour lecture.
