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CM regularity and Kazhdan-Lusztig varieties

Algebra & Discrete Mathematics

Speaker: Colleen Robichaux, University of Illinois at Urbana-Champaign
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Location: 1147 MSB + Zoom (livestream)
Start time: Mon, Sep 27 2021, 11:00AM

We give an explicit formula for the degree of a vexillary Grothendieck polynomial. This generalizes a previous result of J. Rajchgot-Y. Ren-C. Robichaux-A. St. Dizier-A. Weigandt for degrees of symmetric Grothendieck polynomials. We apply our work to compute the Castelnuovo-Mumford regularities of certain matrix Schubert varieties. We also derive formulas for the regularities of Kazhdan-Lusztig varieties coming from open patches of Grassmannians as well as the regularities of mixed one-sided ladder determinantal ideals. This is joint work with Jenna Rajchgot and Anna Weigandt.