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# Dr. Anders Buch, Rutgers – Pieri formulas for the quantum K-theory of cominuscule Grassmannians

## March 31, 2023 @ 4:00 pm - 5:00 pm

Mode:In-Person

Title: *Pieri formulas for the quantum K-theory of cominuscule Grassmannians*

Abstract: The quantum K-theory ring QK(X) of a flag variety X encodes the K-theoretic Gromov-Witten invariants of X, defined as arithmetic genera of Gromov-Witten varieties parametrizing curves meeting fixed Schubert varieties. A Pieri formula means a formula for multiplication with a set of generators of QK(X). Such a formula makes it possible to compute efficiently in this ring. I will speak about a Pieri formula for QK(X) when X is a cominuscule Grassmannian, that is, an ordinary Grassmannian, a maximal orthogonal Grassmannian, or a Lagrangian Grassmannian. This formula has a simple statement in terms of order ideals in a partially ordered set that encodes the degree distance between opposite Schubert varieties. This set generalizes both Postnikovâ€™s cylinder and Proctorâ€™s description of the Bruhat order of X. This is joint work with P.-E. Chaput, L. Mihalcea, and N. Perrin.