Title：Partial groups, Partial categories, and applications to Hall algebras
Speaker:Zongzhu Lin
Institution：Kansas State University, USA
Time：10:30–12:30, May 15, 2025
Location: Seminar Room 5, Mathematics Building, Jilin University
Abstract: 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.
Biography of the Speaker: Zongzhu Lin is a tenured professor and doctoral supervisor at Kansas State University, USA. His research primarily focuses on representation theory, algebraic groups, and quantum groups. He has published dozens of papers in renowned academic journals such as Inventiones Mathematicae, Advances in Mathematics, Transactions of the American Mathematical Society, Communications in Mathematical Physics, and Journal of Algebra. Notable achievements include the Lin-Nakano Theorem, and he has authored five academic monographs.
