The Hypersimplex and the m=2 Amplituhedron - Mathematical Correspondences and Decompositions

Watch a 41-minute lecture from Harvard CMSA's Workshop on Nonlinear Algebra and Combinatorics from Physics where University of Michigan's Melissa Sherman-Bennett explores the relationship between the m=2 amplituhedron and the hypersimplex. Delve into the mathematical correspondence between these two structures - the amplituhedron being a 2k-dimensional subset of Gr(k, k+2) and the hypersimplex being an (n-1)-dimensional polytope in R^n. Learn about joint research that establishes a bijection between decompositions of both structures, originally conjectured by Lukowski-Parisi-Williams. Discover how hypersimplex decompositions connect to matroidal subdivisions, and examine a new proof describing the m=2 amplituhedron as conjectured by Arkani-Hamed-Thomas-Trnka. Explore a novel decomposition of the m=2 amplituhedron into Eulerian-number-many chambers, inspired by similar triangulation principles in hypersimplex geometry.