應(yīng)yl7703永利官網(wǎng)邀請(qǐng)，吉林大學(xué)數(shù)學(xué)學(xué)院生云鶴教授和唐榮博士，廣州大學(xué)數(shù)學(xué)與信息科學(xué)學(xué)院黎允楠副教授將于2021年3月7日舉辦線上學(xué)術(shù)講座，歡迎廣大師生參加。
題目：The controlling $L_\infty$-algebra, cohomology and homotopy of embedding tensors and Lie-Leibniz triples
時(shí)間：3月7日(周日) 上午9:00
騰迅會(huì)議ID: 580 884 761
(鏈接：https://meeting.tencent.com/s/0cWsUwtIFmPH)
摘要：We first construct the controlling algebras of embedding tensors and Lie-Leibniz triples, which turn out to be a graded Lie algebra and an $L_\infty$-algebra respectively. Then we introduce representations and cohomologies of embedding tensors and Lie-Leibniz triples, and show that there is a long exact sequence connecting various cohomologies. As applications, we classify infinitesimal deformations and central extensions using the second cohomology groups. Finally, we introduce the notion of a homotopy embedding tensor which will induce a Leibniz$_\infty$-algebra.
報(bào)告人簡(jiǎn)介: 生云鶴，吉林大學(xué)教授，《數(shù)學(xué)進(jìn)展》編委，吉林省第十六批享受政府津貼專(zhuān)家（省有突出貢獻(xiàn)專(zhuān)家）。2009年1月博士畢業(yè)于北京大學(xué)，從事Poisson幾何、高階李理論與數(shù)學(xué)物理的研究，2019年獲得國(guó)家自然科學(xué)基金委優(yōu)秀青年基金項(xiàng)目，在CMP, IMRN,JNCG,JA等雜志上發(fā)表學(xué)術(shù)論文60余篇，被引用400余次。
題目：An algebraic study of Volterra integral equations and their
operator linearity
時(shí)間：3月7日(周日) 上午10:00
騰迅會(huì)議ID:580 884 761
(鏈接：https://meeting.tencent.com/s/0cWsUwtIFmPH)
摘要：The algebraic study of special integral operators led to the notions of Rota-Baxter operators and shuffle products which have found broad applications such as iterated integrals. In this talk we point out that there are rich algebraic structures underlying Volterra integral operators and the corresponding equations.
First Volterra integral operators with separable kernels can produce a matching twisted Rota-Baxter algebra satisfying twisted integration-by-parts operator identities. To provide a universal space to express general integral equations, free (relative) operated algebras are also constructed in terms of bracketed words and rooted trees with decorations on the vertices and edges.
Utilizing the free construction of matching Rota-Baxter algebras by Gao-Guo-Zhang, further explicit constructions of the free objects in the category of matching twisted Rota-Baxter algebras are given, providing a universal space for separable Volterra equations. As an application, we show that any separable Volterra integral equation is operator linear in the sense that it can be simplified to a linear combination of iterated integrals.
報(bào)告人簡(jiǎn)介: 黎允楠，廣州大學(xué)數(shù)學(xué)與信息科學(xué)學(xué)院副教授，碩士生導(dǎo)師，博士畢業(yè)于華東師范大學(xué)數(shù)學(xué)系，研究方向?yàn)槔畲鷶?shù)、量子群與代數(shù)組合，現(xiàn)與合作者在國(guó)際知名數(shù)學(xué)期刊Mathematische Zeitschrift, Journal of Combinatorial Theory, Series A., Journal of Algebra, Journal of Algebraic Combinatorics等發(fā)表論文數(shù)篇，完成國(guó)家自然科學(xué)基金青年基金項(xiàng)目，主持和參與國(guó)家自然科學(xué)基金面上項(xiàng)目各1項(xiàng)（在研）。2015年成為美國(guó)數(shù)學(xué)會(huì)數(shù)學(xué)評(píng)論網(wǎng)評(píng)論員，2018-2019國(guó)家公派美國(guó)羅格斯大學(xué)研修訪問(wèn)，曾受邀為Advances in Mathematics, European Journal of Combinatorics, Journal of Algebraic Combinatorics, The Ramanujan Journal等國(guó)際知名數(shù)學(xué)期刊審稿。
題目：Relative Rota-Baxter operators and Leibniz bialgebras
時(shí)間：3月7日(周日) 上午11:00
騰迅會(huì)議ID:580 884 761
(鏈接：https://meeting.tencent.com/s/0cWsUwtIFmPH)
摘要： In this talk, first we introduce the notion of a Leibniz bialgebra and show that matched pairs of Leibniz algebras, Manin triples of Leibniz algebras and Leibniz bialgebras are equivalent. Then we introduce the notion of a (relative) Rota-Baxter operator on a Leibniz algebra and construct the graded Lie algebra that characterizes relative Rota-Baxter operators as Maurer-Cartan elements. By these structures and the twisting theory of twilled Leibniz algebras, we further define the classical Leibniz Yang-Baxter equation, classical Leibniz r-matrices and triangular Leibniz bialgebras.
報(bào)告人簡(jiǎn)介:唐榮，吉林大學(xué)師資博士后，2019年博士畢業(yè)于吉林大學(xué)，從事羅巴代數(shù)和代數(shù)結(jié)構(gòu)形變理論方面的研究工作。在Comm. Math. Phys.，J. Algebra，J. Geom. Phys.，J. Algebra Appl.等雜志上發(fā)表論文多篇。
甘肅省應(yīng)用數(shù)學(xué)與復(fù)雜系統(tǒng)重點(diǎn)實(shí)驗(yàn)室
yl7703永利官網(wǎng)
萃英學(xué)院
2021年3月4日
