Yoshinaga Criterion and Topology of Complexified Complement of Real Arrangement

Explore a 45-minute research lecture examining the topology of complexified complements in real arrangements and Yoshinaga's criterion through advanced mathematical concepts. Delve into the cohomology ring of complexified real arrangement complements and their description via the Orlik-Solomon algebra, while investigating the challenges in determining homotopy groups. Learn about Salvetti's homotopy model from the 1980s and its applications in computing complement topology. Examine Yoshinaga's new criterion for determining when higher homotopy groups don't vanish, and discover how it connects to characterizing subarrangements of Type B reflection arrangements. Understand the implementation of algebraic criteria in Macaulay2 and the use of parallel computing for exhaustive searches in hyperplane arrangement families, presented through collaborative research with Graham Denham and Nick Proudfoot at IPAM's Computational Interactions between Algebra, Combinatorics, and Discrete Geometry Workshop.