报告题目：Divided power Hopf algebras（系列报告I-III）

报告简介：

In this series of lectures I will outline the following topics:

(1) As a motivation, I will outline Tate's construction of a free resolution of $R/I$ as an example of strict commutative dg algebra with a divided power structure, computing homology and cohomology of Noetherian rings.

(2) Introduction to general divided power structures and their differential graded extensions. This is useful in crystalline cohomology theory.

(3) Extending the construction of the algebra of symmetric tensors of free modules over commutative modules (also called shuffle algebras) to different graded cases by using trace maps.

(4) Using the functoriality of symmetric tensor constructions, one gets a natural Hopf algebra structure on the algebra of symmetric tensors.

(5) Extending Roby's construction of divided power structures to dg setting.

(6)  Milnor-Moore  theorem on structures of Hopf algebras and Andre theorem on Hopf algebras with divided powers. This algebra will play the role of free $\Gamma$-dg algebras.

(7) Homotopy Lie algebras and its applications to cohomological support varieties of sheaves as associated varieties for representations of Lie algebras.

报告人：林宗柱，1989年在美国马萨诸塞大学获得博士学位，师从代数名家James Humphreys, 现为美国堪萨斯州立大学(Kansas State University )终身教授，主要从事表示论的研究，在Invent. Math., Adv. Math, Comm. Math. Phys等顶级数学期刊上发表论文数十篇。

报告时间：2025年6月25日上午（9:00-11:00）、28下午（3:00-5:00）、30上午（9:00-11:00）。

报告地点：扬州大学瘦西湖校区数学科学学院617报告厅

联系人：李立斌、于志强

欢迎广大师生参加！