談話会: 分類バンディット問題に対する事後サンプルアルゴリズム(田畑公次), Crystalization of K-theoretic Schubert calculus(Travis Scrimshaw)

Event Date: Dec 13, 2022

15:00~16:00 田畑 公次 氏 
16:00~16:30 懇談会
16:30~17:30 Travis Scrimshaw 氏

Place: オンライン開催(Zoom)

田畑 公次/分類バンディット問題に対する事後サンプルアルゴリズム


Travis Scrimshaw/Crystalization of K-theoretic Schubert calculus

Schubert calculus is a now-classical subject that lies at the intersection of algebraic geometry and algebraic combinatorics. However, recent approaches have been to enrich this by replacing the cohomology rings with K-theory rings. We focus on the case of the K-theory of the usual Grassmannian (over C), where there is a nice basis that essentially correspond to the orbits of the invertible upper triangular matrices (called the standard Borel subgroup). We construct polynomial representatives that can be given by combinatorial information. In order to understand these polynomials, we use Kashiwara’s theory of crystal bases to translate the combinatorial information into the representation theory of Lie algebras. We conclude with an application to the Totally Asymmetric Simple Exclusion Process through a last-passage percolation model. No knowledge will be assumed.