Tautological Classes of Matroids

Watch a 52-minute lecture from Harvard CMSA's Workshop on Nonlinear Algebra and Combinatorics from Physics where Chris Eur explores the intersection of algebraic geometry and matroid theory. Discover how algebraic geometry tools have been instrumental in studying matroids, which serve as combinatorial abstractions of hyperplane arrangements. Learn about recent developments in the field and understand how they've remained partially disconnected. Explore the introduction of vector bundles (K-classes) on permutohedral varieties, termed "tautological bundles (classes)" of matroids, which presents a unified framework that recovers and extends recent developments. Examine how this new framework raises intriguing questions about the relationship between combinatorics and geometry, based on joint research with Andrew Berget, Hunter Spink, and Dennis Tseng.