標題：Quantum supersymmetries and two quantum de Rham super complexes
報告時間：2024年11月13日（星期三）14：00-14：45
報告地點：線上騰訊會議（會議ID：90061674）
主講人：胡乃紅
主辦單位：數學與統計學院
報告內容簡介：
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. 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.
主講人簡介：
胡乃紅，華東師范大學數學學院教授、博導，華東師范大學中法基礎數學聯合實驗室LIA執行主任，德國洪堡學者，從事李理論、量子群及Hopf代數結構與表示論研究。現任SCI雜志Frontiers of Mathematics編委。曾獲得教育部霍英東青年教師獎（研究類）二等獎，第三屆教育部優秀教師教學科研獎勵計劃暨教育部青年教師獎，上海市啟明星計劃和追蹤計劃。多次主持國家自然科學基金面上項目，教育部博士點基金項目，兩次參與國家自然科學基金重點項目，并與美國北卡州立大學景乃桓教授合作，獲得國家自然科學基金海外優秀青年合作研究基金（即杰出青年基金B類）支持。在Crelle J.、Comm. Math. Phys.、Israel J. Math.、J. Algebra、J. Pure Appl. Algebra、Pacific J. Math國際著名學術刊物發表論文70篇。
