一、报告题目：Noetherianity of polynomial rings up to actions of groups

二、报告人：李利平 教授

三、报告时间：2026年5月22日（周五）15:30—16:30

四、报告地点：A4-305

报告摘要：Let k be a commutative Noetherian ring, and S a set. It is well known that the polynomial ring A = k[x_s \mid s \in S] is Noetherian if and only if S is a finite set. However, if we consider the natural action of the permutation group G = \mathrm{Sym}(S) on A, then the set of G-invariant ideals of A also satisfies the ascending chain condition; that is, A is Noetherian up to the action of G, or equivalently, A as a left module of the skew group ring A \sharp G is Noetherian. In this talk I will show that this result holds for a big family of subgroups of G satisfying a certain combinatorial condition.

报告人简介：李利平，湖南师范大学数学与统计学院教授、院长。主要研究领域为范畴表示论与表示稳定性理论，在无限组合范畴表示理论的同调方法、一般线性群的同余子群的同调群的线性稳定界限、范畴代数的诺特性判别标准等问题上取得具有国际影响力的成果，被Notices AMS综述文章誉为表示稳定性理论开拓者之一。在Adv. Math., Trans. Amer. Math. Soc., Selecta Math.等期刊发表论文三十余篇，主持多项国家基金，多次担任美国-以色列双边基金会、以色列科学基金会项目评审专家。

欢迎广大师生参加！联系人：51吃瓜网 /数学与交叉科学研究院 杨晓燕