报告题目 (Title)：Polytopes and K-theory of toric and flag varieties （多面体和环面簇以及旗簇的K-理论）

报告人 (Speaker)：Evgeny Smirnov 教授（广东以色列理工学院Guangdong Technion – Israel Institute of Technology）

报告时间 (Time)：2024年1月11日 15:00-16:30

报告地点 (Place)：校本部GJ303

邀请人(Inviter)：张大军 教授

主办部门：理学院数学系

报告摘要：

In 1992 Askold Khovanskii and Alexander Pukhlikov proposed a description of the cohomology ring for a smooth toric variety as the quotient of the ring of differential operators with constant coefficients modulo the annihilator of the volume polynomial for the moment polytope of this variety. Later Kiumars Kaveh observed that the cohomology ring of a full flag variety can be obtained by applying the same construction to Gelfand-Zetlin polytope.

I will speak about our work with Leonid Monin generalizing these results for the case of K-theory. Namely, we describe algebras with a Gorenstein duality pairing as quotients of the ring generated by shift operators. Then we apply this construction to describe the Grothendieck ring of a smooth toric variety; for this we consider shift operators modulo the annihilator of the Ehrhart polynomial of the moment polytope (this substitutes the volume polynomial). Finally, this construction can be generalized to the case of full flag varieties of type A. This description allows us to make computations in the Grothendieck ring of a full flag variety by intersecting faces of Gelfand-Zetlin polytopes; this generalizes our result with Valentina Kiritchenko and Vladlen Timorin.