报告题目：Two quantum de Rham super complexes and stratification Theorem

报告简介：In order to study the ``modular" representation theory of quantum gl(m|n) at root of unity, we introduce the quantum Manin supersapce and quantum (dual) Grassmann superalgebra with quantum divided power structure, and develop a kind of quantum differential calculus over them, and construct two kinds of quantum de Rham super complexes: one is of infinite length which is the quantized version of the classical analogue due to Manin-Deligne-Morgan in their early study of supermanifolds from gauge field theory, another is of finite length which has no classical analogue to our knowledge. For the latter, we prove the Poincare lemma for nontruncated complex, while for the truncated case, in order to calculate all the qauntum de Rham cohomologies we need to develop a specific technique to overcome the complicated difficulties encountered  in the quantum supercase. I'll also talk about the ``$\ell$-adic phenomenon" occurred in  a kind of indecomposable modules in the root of unity case which originally were irreducible modules in the generic case. This talk is based on a series of our joint work with Dr. Ge Feng, and Prof. Marc Rosso.

报告人： 胡乃红，华东师范大学数学科学学院教授、博士生导师、德国洪堡学者。主要研究方向是李理论、量子群及Hopf代数结构分类与表示论，近年来对有限张量范畴理论及拓扑量子计算感兴趣。多次主持国家自然科学基金面上项目，教育部博士点基金项目，并与美国北卡州立大学景乃桓教授合作，获得国家自然科学基金海外优秀青年合作研究基金(即杰出青年基金B类)支持。在Crelle J.、Comm. Math. Phys.、Israel J. Math.、J. Algebra、JPAA、Pacific J. Math等国际著名学术刊物发表论文65篇，培养毕业博士20人，分别从事李代数表示论、循环同调论、量子群结构与表示论、Hopf代数分类、高阶范畴表示论、有限张量范畴分类等方面研究。

报告时间：2025年6月24日（星期二）上午 10：30-11:30

报告地点：数学科学学院617会议室

主办单位：扬州大学数学科学学院

联系人：李立斌 于志强

欢迎广大师生参加！