LACIM: K-theoretic Catalan functions

Abstract: Schubert calculus connects problems in algebraic geometry to combinatorics, classically resolving the question of counting points in the intersection of certain subvarieties of the Grassmannian with Young Tableaux. Subsequent research has been dedicated to carrying out a similar program in more intricate settings. A recent breakthrough in the Schubert calculus program concerning the homology of the affine Grassmannian and quantum cohomology of flags was made by identifying k-Schur functions with a new class of symmetric functions called Catalan functions. In this talk, we will discuss a K-theoretic refinement of this theory and how it sheds light on K-k-Schur functions, the Schubert representatives for the K-homology of the affine Grassmannian.

Date published: Friday, March 19, 2021