报告人：李海生 （美国罗格斯大学肯顿分校 教授）
报告时间：2024年12月 20、21、22、23日 上午9：00-11：00
1、20日上午9：00-11：00 #腾讯会议：518-268-211密码123456
2、21日上午9：00-11：00 #腾讯会议：891-583-483密码123456
3、22日上午9：00-11：00#腾讯会议：828-671-402密码123456
4、23日上午9：00-11：00#腾讯会议：926-718-200密码123456
联系人：陈海波 副教授
欢迎广大师生参加！
报告摘要： In this short course, we shall study some natural associations of Lie algebras with vertex algebras. Roughly speaking, each association is attached to a particular vertex algebra representation theory, or equivalently, a theory of “modules.” In literature, there are theories of modules (including weak modules, Z-graded modules, and admissible modules for a VOA), twisted modules, quasi modules, equivariant quasi modules, ϕ-coordinated (quasi) modules, and twisted ϕ-coordinated (quasi) modules. In practice, to associate a certain (infinite-dimensional) Lie algebra with vertex algebras we shall need suitably to choose a particular representation theory. In the first lecture, we first present the vertex algebra basics, including the definitions of a vertex algebra and a module for a vertex algebra, and then present the conceptual construction of vertex algebras and modules. In the second lecture, we study natural associations of vertex algebras and modules with some better known Lie algebras including (untwisted) affine Lie algebras, the Virasoro algebra, and the (N =1) Neveu-Schwarz superalgebra. In the third lecture, we study twisted modules for vertex (super)algebras, and present the conceptual construction of vertex superalgebras and twisted modules. In the forth lecture, we study the association of vertex superalgebras and twisted modules to twisted affine Lie algebras and the (N =1) Ramond superalgebra.
报告人简介：李海生，美国罗格斯大学肯顿分校终身教授，著名华人数学家、顶点算子代数奠基人之一，多年来一直从事无穷维李代数、顶点代数、顶点算子代数的重要表示与结构理论的研究。在Duke Math. J.、Adv. Math.、Math. Ann.、Comm. Math. Phys.、Trans. Amer. Math. Soc.、Israel J. Math.、Math. Z.、Selecta Math. (N.S.)、J. Algebra、J. Pure Appl. Algebra等著名期刊发表高水平学术论文100余篇，被同行文章引用超3000篇次，并担任Electronic Research Archive杂志的编委。主持多项美国自然科学基金，一项中国自然科学基金（海外合作项目）。
