標(biāo)題：Quantum supersymmetries and two quantum de Rham super complexes
報(bào)告時(shí)間：2024年11月13日（星期三）14：00-14：45
報(bào)告地點(diǎn)：線(xiàn)上騰訊會(huì)議（會(huì)議ID：90061674）
主講人：胡乃紅
主辦單位：數(shù)學(xué)與統(tǒng)計(jì)學(xué)院
報(bào)告內(nèi)容簡(jiǎn)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(jiǎn)介：
胡乃紅，華東師范大學(xué)數(shù)學(xué)學(xué)院教授、博導(dǎo)，華東師范大學(xué)中法基礎(chǔ)數(shù)學(xué)聯(lián)合實(shí)驗(yàn)室LIA執(zhí)行主任，德國(guó)洪堡學(xué)者，從事李理論、量子群及Hopf代數(shù)結(jié)構(gòu)與表示論研究?，F(xiàn)任SCI雜志Frontiers of Mathematics編委。曾獲得教育部霍英東青年教師獎(jiǎng)（研究類(lèi)）二等獎(jiǎng)，第三屆教育部?jī)?yōu)秀教師教學(xué)科研獎(jiǎng)勵(lì)計(jì)劃暨教育部青年教師獎(jiǎng)，上海市啟明星計(jì)劃和追蹤計(jì)劃。多次主持國(guó)家自然科學(xué)基金面上項(xiàng)目，教育部博士點(diǎn)基金項(xiàng)目，兩次參與國(guó)家自然科學(xué)基金重點(diǎn)項(xiàng)目，并與美國(guó)北卡州立大學(xué)景乃桓教授合作，獲得國(guó)家自然科學(xué)基金海外優(yōu)秀青年合作研究基金（即杰出青年基金B(yǎng)類(lèi)）支持。在Crelle J.、Comm. Math. Phys.、Israel J. Math.、J. Algebra、J. Pure Appl. Algebra、Pacific J. Math國(guó)際著名學(xué)術(shù)刊物發(fā)表論文70篇。
