报告题目：Quantum supersymmetries and two quantum de Rham super complexes

主讲人：胡乃红 教授（华东师范大学）

摘要：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. If time permits, 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.

报告时间：2024年12月21日上午08:00 - 08:50

报告地点：数学科学学院301室

报告人简介：

胡乃红，华东师范大学数学学院教授、博导，华东师范大学中法基础数学联合实验室LIA执行主任，德国洪堡学者，从事李理论、量子群及Hopf代数结构分类与表示论研究，近年来对有限张量范畴理论及拓扑量子计算感兴趣。曾获得教育部霍英东青年教师奖（研究类）二等奖，第三届教育部优秀教师教学科研奖励计划暨教育部青年教师奖，上海市启明星计划和追踪计划。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，两次参与国家自然科学基金重点项目，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，其中3人获得上海市优秀博士论文成果奖，2人荣获全国百篇优秀博士论文提名奖，3人获得国家优秀博士奖学金。多人获得省部级人才项目（获浙江省151人才计划第二层次、天山计划学者、上海市东方学者计划）和国家基金支持，并成为教授博导及科研教学骨干。