37000gcom威尼斯2023年第 28期数理大讲堂

报告题目：An introduction to affine Grassmanian and its applications

报告人：洪久族教授（University of North Carolina at Chapel Hill）

报告时间：2023年7月31日10：00-11：00

报告地点：37000gcom威尼斯3号楼3B205

摘要：An affine Grassmannian is an infinite dimensional generalization of Grassmannian and flag manifold. It plays important roles in representation theory and geometric Langlands program. For example, the global sections of line bundles on affine Grassmannian give rise to integrable representations of affine Lie algebras, and the restrictions to Schubert varieties give rise to Demazure modules. The study of singularies of Schubert varieties in affine Grassmannian is also an important question. On one hand, their singularies are related to Kazhdan-Lusztig polynomials; on the other hand, their intersection cohomologies carry irreducible representations of the Langlands dual group via the so called geometric Satake correspondence. In my talk, I will start with usual Grassamnian/flag manifolds as a motivation, and will focus on the affine Grassmanian of GL_n. If time permits, I will also talk about my research related to twisted affine Grassmannians.

报告人简介：洪久族教授，泰顺人，现任北卡大学副教授（tenured），2012年在以色列特拉维夫大学获博士学位，2012-2015在耶鲁大学任Gibbs assistant professor。