报告题目：Symmetric Noetherianity of polynomial rings

主讲人：李利平 教授（中国科学技术大学）

摘要：Let $k$ be a commutative Noetherian ring, $S$ a set, and $A = k[x_s \mid s \in S]$. Hilbert's basis theorem asserts that $A$ is Noetherian if and only if $|S|$ is finite. Recently, people showed that $A$ is Noetherian with respect to the action of $\mathrm{Sym}(S)$; that is, ideals invariant under the action of $Sym(S)$ satisfy the ACC. In this talk I will explain that this result actually holds for many much smaller subgroups of $\mathrm{Sym}(S)$ via a sheaf theoretic approach on ringed sites. As an interesting byproduct, we obtain a new equivalent statement of the Axiom of Choice. This work is joint with Peng and Yuan.

报告时间：2024年12月28日上午08:00 - 08:50

报告地点：数学科学学院301室

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重要成果，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。