Math and Stats Colloquium: Convex Geometry of Building Sets

Friday, Nov. 22, 2024, 4–5 p.m.

Rick Danner - University of Vermont

Title: Convex Geometry of Building Sets

Abstract: Building sets were introduced in the study of wonderful compactifications of hyperplane arrangement complements and were later generalized to finite meet-semilattices. Convex geometries, the duals of antimatroids, offer a robust combinatorial abstraction of convexity. Supersolvable convex geometries and antimatroids appear in the study of poset closure operators, Coxeter groups, and matroid activities. We prove that the building sets on a finite meet-semilattice form a supersolvable convex geometry. As an application, we demonstrate that building sets and nested set complexes respect certain restrictions of finite meet-semilattices unifying and extending results of several authors. This is joint work with Spencer Backman.

Mathematics and Statistics Colloquium Series