Cristian Lenart, part 1, `A Chevalley formula for the K-theory of semiinfinite flag manifolds'

Abstract: With S. Naito and D. Sagaki, I proved a combinatorial multiplication formula of Chevalley type for the equivariant K-theory of semi-infinite flag manifolds; these are certain affine versions of finite flag manifolds G/B. Our formula is expressed in terms of the so-called quantum alcove model, which is based on Weyl group combinatorics. It implies a Chevalley type formula for the equivariant quantum K-theory of G/B. I will discuss these formulas, as well as several applications of them and related results, including the solutions to some longstanding conjectures.