Abstract:
The generalized coinvariant algebra \$R_{n,k}\$ of Haglund–Rhoades–Shimozono is a well-studied object in representation theory. Pawlowski–Rhoades constructed the variety of spanning line configurations \$X_{n,k}\$, whose cohomology ring is isomorphic to \$R_{n,k}\$. In this talk, we show that the \$K_0\$-ring of \$X_{n,k}\$ is also canonically isomorphic to \$R_{n,k}\$. We explore the question of when the \$K_0\$-ring of a variety is abstractly isomorphic to its Chow ring, providing a counterexample even when the variety is assumed to be smooth and paved by affines. We then discuss word-Schubert, word-Grothendieck polynomials, and rectangular pipe dreams, generalizing many aspects of Schubert calculus of the flag variety to \$X_{n,k}\$. Based on arXiv:2512.22769.
Note: This talk begins with a pre-seminar (aimed at graduate students) at 3:30–4:00. The main talk starts at 4:10.
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Meeting ID: 915 4733 5974