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Tuesday, October 13, 2020

**Abstract:** Matrix Schubert varieties are the orbits of $B\times B$ acting on all n-by-n matrices, where $B$ is the group of invertible lower triangular matrices. Knutson and Miller identified a Gröbner basis for the prime ideals of these varieties. They also showed that the corresponding initial ideals are Stanley-Reisner ideals of shellable simplicial complexes. Skew-symmetric matrix Schubert varieties are the nonempty intersections of matrix Schubert varieties with the subspace of skew-symmetric matrices, and in this talk I will discuss some new extensions of Knutson and Miller's results to this setting. In particular, I will describe a natural Gröbner basis for the prime ideals of skew-symmetric matrix Schubert varieties, along with a primary decomposition for the corresponding initial ideals involving certain involution pipe dreams. As one application, this will lead to a geometric explanation for some recent formulas for involution Schubert polynomials. This is joint work with Zachary Hamaker and Brendan Pawlowski. Please email Colleen at cer2 (at) illinois (dot) edu for the Zoom ID and password.