1-Skeleton Posets of Bruhat Interval Polytopes

Learn about 1-skeleton posets of Bruhat interval polytopes in this 34-minute research lecture from Harvard CMSA's Workshop on Nonlinear Algebra and Combinatorics from Physics. Explore how Bruhat interval polytopes emerge as moment map images of toric varieties and totally positive spaces in flag variety. Delve into the study of 1-skeleta of these polytopes as posets that bridge weak order and Bruhat order, examining cases where these posets form lattices despite the polytopes not being simple. Discover the connection to bridge polytopes through Williams' work, where chains in the 1-skeleton poset correspond to BCFW-bridge decompositions of plabic graphs. Cover key concepts including Bruhat order, structural properties, general communication, color quotients, equivalence classes, minimal maximum elements, weak order, lattice operations, and H-vectors.