Combinatorics Seminar: K-theoretic Schubert Calculus for Orthogonal Orbits

Event details Date: Monday, October 26, 2026 Time: 1:00 PM to 2:00 PM Location: Kaprielian Hall (KAP) - 414 - 3620 South Vermont Avenue, Los Angeles, CA 90089 Type: Lecture / Talk / Workshop Campus: University Park Campus Department: Mathematics About this event Jiayi Wen, USC Title: K-theoretic Schubert Calculus for Orthogonal Orbits Abstract: Let G be a connected complex reductive group and B be a Borel subgroup. A subgroup H is called spherical if H acts on G/B with finitely many orbits. Brion gave an explicit formula to express the cohomology classes of H-orbits as linear combinations of Schubert cycles. The coefficients of Schubert cycles are nonnegative integers related to some combinatorial properties of weak orders. However, when one replaces the cohomology ring by the algebraic K-theory of coherent sheaves on G/B, the story becomes complicated and no general formula for H-orbits is available. In this talk, we will focus on the case when G is the general linear group, and H is the orthogonal subgroup in G. We will explore some new results in K-theory when the H-orbits are indexed by vexillary involutions, where the orbit closures have rational singularities. Official event details: https://calendar.usc.edu/event/combinatorics-seminar-k-theoretic-schubert-calculus-for-orthogonal-orbits