Anna Weigandt – Weak order on alternating sign matrix varieties

Speaker: Anna Weigandt (University of Minnesota) Title: Weak order on alternating sign matrix varieties Abstract: Alternating sign matrices (ASMs) form the MacNeille completion of the strong Bruhat order on the symmetric group. There is a natural interpretation of this poset as the containment order on ASM varieties, which are generalized determinantal ideals. In 2018, Hamaker and Reiner defined weak Bruhat order on ASMs, which when restricted to the symmetric group, is the usual weak order. We initiate a geometric study of weak order on ASMs varieties, focusing on how combinatorial properties of this poset describe geometric properties of ASM varieties. This is joint work with Laura Escobar and Patricia Klein. Thematic program "Algebraic combinatorics and applications" Center for Mathematics at Notre Dame June 29 – July 10, 2026 sites.nd.edu/cmnd2026-thematic-program Mathematics at Notre Dame: math.nd.edu