时间：8：00-12：00       腾讯会议 970 852 357

主讲人：周国栋教授 华东师范大学 8:00-9:00 

报告题目：Characterising higher Auslander (Gorenstein) algebras via abelianess of    modules of finite (Gorenstein) projective dimensions

报告摘要：It is well known that there is a nice connection between artin algebras of finite representation type and Auslander algebras. For Auslander algebras, the category of all projective modules is an abelian category and so there is a close relationship between the abelianness of this category and being of finite representation type. Now let n be a positive integer. To get a higher dimensional analog of this connection, we characterize n-Auslander algebras by the abelianness of the category of all modules with projective dimension less than n and then by higher Auslander correspondence we obtain a new characterization of the class of artin algebras having n-cluster tilting modules. This talk is based on a joint work with Mohammad Keshavarz.

报告人简介：周国栋，华东师范大学金沙集团wwW3354CC教授、副院长，博士毕业于法国亚棉大学，师从著名代数学家Alexander Zimmermann教授。主要研究领域为代数表示论与同调代数。完成国家自然科学基金青年基金、上海市浦江人才计划项目、教育部博士点新教师基金，主持在研国家自然科学基金面上项目两项，其学术成果发表在J. London Math. Soc.、Math. Z.、Trans. Amer. Math. Soc.、IMRN、J. Algebra、J. Noncommut. Geom. Proc. Royal Edinburgh Soc. Section A: Math.等国际著名期刊上。

主讲人：胡乃红教授 华东师范大学 9:00-10:00 

报告题目：Quantum group and a generalization of Jones polynomial.

报告摘要：In this talk, we will recall some seminal works which currently serve as the     fundamental stone of tensor categories from TQFT and quantum knot invariants from quantum groups and Hopf algebras.  As applications, we give a kind of quantum knots invariants from an object I obtained twenty years ago, the so-called n-rank Taft algebra, which is a generalization of the Jones polynomials. Also we get some interesting byproducts.

报告人简介：胡乃红，华东师大数学系教授，博士生导师，德国洪堡学者，从事李代数与量子群的结构与表示论研究。已在国际学术刊物发表论文60余篇。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。

主讲人：生云鹤教授 吉林大学 10:00-11:00 

报告题目：Post-Hopf algebras, relative Rota-Baxter operators and solutions of the Yang-Baxter equation

报告摘要：We introduce the notion of a post-Hopf algebra, which gives rise to a post-Lie algebra on the space of primitive elements and there is naturally a post-Hopf algebra structure on the universal enveloping algebra of a post-Lie algebra. A novel property is that a cocommutative post-Hopf algebra gives rise to a generalized Grossman-Larsson product, which leads to a subadjacent Hopf algebra and can be used to construct solutions of the  Yang-Baxter equation. Then we introduce the notion of relative Rota-Baxter operators on   Hopf algebras.

A cocommutative post-Hopf algebra gives rise to a relative Rota-Baxter operator on its subadjacent Hopf algebra. Conversely,  a relative Rota-Baxter operator also induces a post-Hopf algebra. Then we show that relative Rota-Baxter operators give rise to matched pairs of Hopf algebras. Consequently, post-Hopf algebras and relative Rota-Baxter operators give solutions of the Yang-Baxter equation in certain cocommutative Hopf algebras. Finally we characterize   relative Rota-Baxter operators on Hopf algebras using relative Rota-Baxter operators on the Lie algebra of primitive elements, graphs and  module bialgebra structures.

报告人简介：生云鹤，吉林大学教授，《数学进展》、《J. Nonlinear Math. Phys.》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,Adv.Math.,IMRN,JNCG,JA等杂志上发表学术论文70余篇，被引用500余次。

主讲人：高兴教授 兰州大学 11:00-12:00

报告题目：Compatible structures of operads, Manin products and Koszul duality

报告摘要：Various compatibility conditions among replicated copies of operations in a given algebraic structure have appeared in broad contexts in recent years. Taking an uniform approach, this paper gives an operadic study of compatibility conditions for nonsymmetric operads with unary and binary operations, and homogeneous quadratic and cubic relations. This generalizes the previous studies for binary quadratic operads. We consider three compatibility conditions, namely the linear compatibility, matching compatibility and total compatibility, with increasingly strict restraints among the replicated copies. The linear compatibility is in Koszul dual to the total compatibility, while the matching compatibility is self dual. Further, each compatibility can be expressed in terms of either one or both of the two Manin square products. It is shown that compatible structures of the operads for associative algebra and differential algebra are Koszul utilizing rewriting systems.

报告人简介：高兴，博士，兰州大学“萃英学者”、教授，博士生导师。于2010年7月在兰州大学数学与统计学院获得博士学位，留校工作至今。在2015年8月至2016年8月间，在美国Rutgers大学交流访问。主要从事Rota-Baxter代数和代数组合等领域的研究， 发表SCI学术论文四十余篇，主持数学天元基金、青年科学基金、国家自然科学基金面上项目和甘肃省自然科学基金项目, 获甘肃省自然科学奖二等奖，出版教材一本。