报告题目：Partial groups, Partial categories, and applications to Hall algebras
报 告 人：Zongzhu Lin
所在单位：Kansas State University, USA
报告时间：2025年5月15日 10:30-12:30
报告地点：吉林大学数学楼第5研讨室
报告摘要: Alperin studied the fusion properties of subgroups of a Sylow p-subgroup of finite group in 1967, which lead to later development of fusion systems. Fusion system is regarded as a local group theory. In the attempt to characterize fusion systems in terms of homotopy theory, the concept of localities and partial groups were introduced. Around the same time Kriz and May also introduced partial algebras in an attempt to formalize the intersection multiplication of motives. It turns out that both concepts are pretty much the same in categorical setting, where multiplications need not to be defined as they should. To do so one has to define the concepts of domains in both settings. The concept of partial categories can be defined in a similar fashion. Partial categories can be used as a framework to bridge several different mathematical structures. In this talk, I will focus on realizing Hall algebras of an abelian category as the Grothendieck ring of a partial category attached to the abelian category. This is an attempt to investigate the relations between Hall algebras and cohomology theory of simplicial sets.
报告人简介：林宗柱，美国堪萨斯州立大学终身教授，博士生导师，主要从事表示论、代数群以及量子群等方面的研究，在 Invent. Math.，Adv. Math., Trans. Amer. Math. Soc., CMP 和J. Algebra 等重要学术期刊上发表论文数十篇，标志性成果包括林-Nakano定理，出版学术著作五部。
