报告人：李利平教授

        湖南师范大学

报告题目：Shift functor and its application in representation theory of infinite categories

报告时间：11月11日下午3点

报告地点：海韵数理楼661

联系人： 余铌娜助理教授

报告摘要：

Representation theory of infinite categories has provided a uniform approach for representation stability theory, a new active area investigating the asymptotic behaviors of representations of a sequence of groups (for instance, symmetric groups, general linear groups, etc.). It has been observed that many interesting categories in representation stability theory, such as FI (the category of finite sets and injections), VI (the category of finite dimensional vector spaces and linear injections), are equipped with self-embedding functors, inducing shift functors in their module categories.

In this talk we describe a formal procedure establishing various properties for representations of categories equipped with nice shift functors. Explicitly, if a property (P) of representations (for instance, finitely presented property, having finite projective dimension, etc.) behaves well under the shift functor, then all finitely generated modules over Noetherian rings satisfy (P). In particular, we obtain a few easy criteria guaranteeing important properties such as Noetherianity, finite Castelnuovo-Mumford regularity, and polynomial grwoth property.

报告人简介：1999年毕业于清华大学化学系本科，2012年获明尼苏达大学数学博士学位。2015年起任湖南师范大学特聘教授。研究领域包括代数表示论、同调代数、非交换环等，目前主要研究方向为无限范畴基于一般交换环上的表示及其在表示稳定性理论中的应用。

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