A brief introduction to representation stability theory
摘要：Representation stability theory, introduced by Thomas Church and Benson Farb in 2010, explores the asymptotic behavior of a sequence of representations of groups (such as symmetric groups, general linear groups, etc.), and is widely applied to investigate properties of (co)homology groups of many important examples like configuration spaces, congruence subgroups, mapping class groups in geometric group theory, algebraic topology and algebraic geometry. Recently this theory was categorified via introducing some infinite discrete categories with particular combinatorial structure and stuying their representations. In this talk I will describe the motivation, background, current developent of this theory, as well as my own contribution.