Move-Reduced Graphs on a Torus vs Positroid Catalan Numbers

Explore the intersection of combinatorial dynamics and algebraic geometry in this 50-minute lecture presented by Pavel Galashin at IPAM's Integrability and Algebraic Combinatorics Workshop. Delve into the applications of affine symmetric group dynamics to two distinct problems: classifying move-reduced bipartite graphs on a torus and computing positroid Catalan numbers. Discover how these seemingly unrelated topics connect through shared mathematical structures. Gain insights into the geometry of positroid varieties in the Grassmannian and their relevance to knot theory. Examine the collaborative research findings of Galashin, George, and Lam in this advanced exploration of algebraic combinatorics and its applications.