The direct sum morphism in (equivariant) Schubert calculus

Abstract: Direct sum of subspaces defines a map on Grassmannians, which, after taking an appropriate limit, leads to a product-like structure on the infinite Grassmannian. The corresponding cohomology pullback coincides with a famous co-product on the ring of symmetric functions. I’ll describe torus-equivariant extensions of this setup, along with positivity results for structure constants, and some open questions. This story partially extends work by Thomas-Yong, Knutson-Lederer, and Lam-Lee-Shimozono, and connects to joint work with W. Fulton. (No special knowledge of Schubert calculus -- equivariant or not -- will be assumed.)

algebraic geometry

Audience: researchers in the topic

( slides | video )

Stanford algebraic geometry seminar

Series comments: The seminar was online for a significant period of time, but for now is solely in person. More seminar information (including slides and videos, when available): agstanford.com