Combinatorics Seminar

In 2018, Hamaker and Reiner generalized the notions of weak order and descent sets from permutations to alternating sign matrices (ASMs). As one associates a matrix Schubert variety to a permutation, one can more generally associate an intersection of matrix Schubert varieties (now called ASM varieties) to an ASM. In this talk, we will review the role of matrix Schubert varieties - and their unions and intersections - in Schubert calculus and describe classical uses of the permutation matrices and strong Bruhat order in encoding algebro-geometric invariants. We will then describe new work giving relationships between poset combinatorics and algebro-geometric invariants determined by the ASMs under weak order. This is joint work with Laura Escobar and Anna Weigandt.

https://arxiv.org/abs/2502.19266