李理论与张量范畴研讨会

(扬州 2023年9月27日)

会议日程

地点：扬州大学瘦西湖校区56号楼数学科学学院204会议室

报告人简介及报告摘要：

    谭绍滨，厦门大学教授, 博士生导师，闽江学者特聘教授。博士毕业于加拿大Saskatchewan大学，加拿大Fields数学研究所博士后。现任厦门大学数学科学学院院长，曾任厦门大学校长助理、教务处处长、国际合作与交流处处长、台港澳事务办公室主任。担任第六、七届国务院学位委员会数学学科评议组成员。现任中国数学会常务理事、福建省数学会副理事长、教育部高等学校教学指导委员会委员。担任“Acta Mathematica Sinica”、“Journal of Mathematical Study”、《数学进展》、《应用数学》等学术期刊编委。曾获国防科工委科技进步一等奖、宝钢优秀教师奖、福建省第五届青年科技奖、福建省第五届高等学校教学名师奖、福建省自然科学二等奖。现主持国家自然科学基金重点项目、国家自然科学基金数学天元项目。

   报告摘要：The extended affine Lie algebras(EALAs) are higher rank generalization of the finite dimensional simple Lie algebras and affine Kac-Moody algebras over the field of complex numbers, and the toroidal EALAs are one class of the most important EALAs. In this talk, we deal with the classification of irreducible integrable representations for the elliptic Lie algebras, that is the toroidal EALAs of nullity two. The talk is based on the work with Fulin Chen and Zhiqiang Li.

  余铌娜，厦门大学教授，加州大学圣克鲁兹分校博士；加州大学河滨分校博士后，主要研究顶点算子代数及无穷维李代数，在Communications in Mathematical Physics，Proceedings of the American Mathematical Society， Journal of Algebra，Journal of Pure and Applied Algebra等期刊上发表论文10余篇

      报告摘要：In [Adamovic-Lam-Pedic-Yu; 2019], we generalized Dong-Mason's theorem on irreducibility modules for cyclic orbifold vertex algebra to the entire category weak modules and applied these results to Whittaker modules. In this talk, I will present further generalizations of these results for nonabelian orbifolds of vertex operator superalgebras. I will also talk about applications of these results to examples and give irreducibility of modules of Whittaker type for orbifolds of vertex (super)algebras. This talk is based on a joint work with Drazen Adamovic, Ching Hung Lam and Veronika Pedic Tomic.

   董崇英，美国加州大学Santa Cruz分校终身教授、数学系原系主任，国际上无限维李代数和顶点算子代数领域最杰出的数学家之一，多年来一直从事无穷维李代数和顶点算子代数研究，在顶点算子代数、Orbifold理论以及广义月光等方面的研究做出了重要的工作。在Acta Math.、Duke Math. J.、Adv. Math.、Comm. Math. Phys.等国际著名期刊发表论文100多篇，总引用超过3000次，其中包括Fields奖获得者Drinfeld、Zelmanov和Borcherds以及著名数学家如Beilinson和Kac等人的重要引用。

报告摘要：This introductory talk will survey the recent development of the monstrous moonshine. Conjectured by McKay-Thompson-Conway-Norton and proved by Borcherds, the moonshine conjecture reveals a deep connection between the largest sporadic finite simple group Monster and genus zero functions.  From the point of view of vertex operator algebra, moonshine is a connection among finite groups, vertex operator algebras and modular forms. This talk will explain how the moonshine phenomenon  can be understood in terms of orbifold theory.

    任丽，四川大学数学学院教授。主要研究领域为李代数和顶点算子代数，在Adv. Math.、Trans. Amer. Math. Soc.、J. Algebra等著名SCI杂志发表论文20多篇。主持国家自然科学基金面上项目和青年项目、国家博士后特别基金等项目。

       报告摘要：A modular tensor category is pointed if every simple object is a simple current.  We show that any pointed modular tensor category is equivalent to the module category of a lattice vertex operator algebra. Moreover, if the module category C of a twisted Drinfeld double associated to a finite abelian group G and a 3-cocycle is pointed, then there exists a selfdual positive definite even lattice L such that G can be realized an automorphism group of lattice vertex operator algebra $V_L,$  and C is equivalent to the module category of $V_L^G.$ This is a joint work with C.Dong and S. Ng