应数学与统计学院邀请，吉林大学数学学院生云鹤教授和唐荣博士，广州大学数学与信息科学学院黎允楠副教授将于2021年3月7日举办线上学术讲座，欢迎广大师生参加。

题目：The controlling $L_\infty$-algebra, cohomology and homotopy of embedding tensors and Lie-Leibniz triples

时间：3月7日(周日) 上午9:00

腾迅会议ID: 580 884 761

(链接：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.

报告人简介: 生云鹤，吉林大学教授，《数学进展》编委，吉林省第十六批享受政府津贴专家（省有突出贡献专家）。2009年1月博士毕业于北京大学，从事Poisson几何、高阶李理论与数学物理的研究，2019年获得国家自然科学基金委优秀青年基金项目，在CMP, IMRN,JNCG,JA等杂志上发表学术论文60余篇，被引用400余次。

题目：An algebraic study of Volterra integral equations and their

operator linearity

时间：3月7日(周日) 上午10:00

腾迅会议ID:580 884 761

(链接：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.

报告人简介: 黎允楠，广州大学数学与信息科学学院副教授，硕士生导师，博士毕业于华东师范大学数学系，研究方向为李代数、量子群与代数组合，现与合作者在国际知名数学期刊Mathematische Zeitschrift, Journal of Combinatorial Theory, Series A., Journal of Algebra, Journal of Algebraic Combinatorics等发表论文数篇，完成国家自然科学基金青年基金项目，主持和参与国家自然科学基金面上项目各1项（在研）。2015年成为美国数学会数学评论网评论员，2018-2019国家公派美国罗格斯大学研修访问，曾受邀为Advances in Mathematics, European Journal of Combinatorics, Journal of Algebraic Combinatorics, The Ramanujan Journal等国际知名数学期刊审稿。

题目：Relative Rota-Baxter operators and Leibniz bialgebras

时间：3月7日(周日) 上午11:00

腾迅会议ID:580 884 761

(链接：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.

报告人简介:唐荣，吉林大学师资博士后，2019年博士毕业于吉林大学，从事罗巴代数和代数结构形变理论方面的研究工作。在Comm. Math. Phys.，J. Algebra，J. Geom. Phys.，J. Algebra Appl.等杂志上发表论文多篇。

甘肃省应用数学与复杂系统重点实验室

数学与统计学院

萃英学院

2021年3月4日