报告题目 (Title)：Representation theory and noncommutative geometry
中文标题：表示论和非交换几何
报告人 (Speaker)：林宗柱 教授 （美国堪萨斯州立大学）
报告时间 (Time)：2025年7月4日（周五）10：00am
报告地点 (Place)：校本部 GJ303
邀请人(Inviter)：张红莲和黄红娣
报告摘要：Given an affine algebraic scheme X, the closed geometric points are irreducible representations. Let C be the category of quasi-coherent sheaves, which is exactly the category of A-modules if X=Spec(A). Although C is a symmetric monoidal category, Rosenberg gave a reconstruction of the scheme X from the abelian category C. Rosenberg's construction applies to much wider abelian categories (or even exact categories). There is also another reconstruction of X when X is a smooth algebraic variety in terms of the monoidal triangulated tensor category of perfect complexes by Balmer, using thick prime tensor ideals. In this talk I will compare the two constructions when X is a smooth algebraic variety X and propose approaches in noncommutative cases. For not necessarily symmetric triangulated tensor categories, Nakan,Vashaw and Yakimov has constructed a Balmer spectrum. It is an interesting question to compare NVY construction with that of Rosenberg.