走向现代数学学术报告 - 舒成博士（No. 914)

报告题目：The tame Deligne-Simpson problem

报告时间：2026年3月12日 16:00

报告地点：东海岸校区-D实209

报 告 人：舒成 博士（西湖大学）

邀 请 人：陈哲 副教授

报告摘要：In this talk, we explain a recent solution to the long-standing problem of Deligne-Simpson: given conjugacy classes (C_j)_{1<= j<= k} of invertible matrices of rank n, do there exist A_j \in C_j such that (1) A_1 \cdots A_k = Id and (2) there is no nontrivial proper subspace of \mathbb{C}^n that is preserved by every A_j? A conjectural necessary and sufficient condition on (C_j)_j in terms of certain Kac-Moody root systems was proposed by Crawley-Boevey, and the sufficiency statement was later proved in his joint work with Shaw. Our main result proves the necessity statement and the method is a combination of nonabelian Hodge theory and variation of stability conditions.

报告人简介：舒成，2020年博士毕业于法国巴黎七大（Université Paris Diderot，现更名Université Paris Cité），目前在西湖大学任博士后。主要研究几何表示论，包括非连通李型群的特征标、特征标簇及其关联多项式。相关工作发表于 Adv Math、Forum Math Sigma、J Alg 等期刊。