Secondary polytopes and L_∞ algebras
数学专题报告
报告题目(Title)：Secondary polytopes and L_∞ algebras
报告人(Speaker)：李龙飞（堪萨斯州立大学）
地点(Place)：北京师范大学后主楼1220报告厅
时间(Time)：2024年7月3日 10:00-11:30
邀请人(Inviter)：刘玉明
报告摘要
We start with introducing the general background on secondary polytopes, a dual language of polygons. Since each face of secondary polytopes is itself a product of several secondary polytopes from a certain subdivision of the initial one, the chain complex of the secondary polytopes looks like a dg-algebra. Then we will talk about the L_∞-algebra structure in the space g_A spanned by polytopes with vertices in a given set A in R^d. By defining a differential in the symmetric algebra generated by shifted dual space to g_A, the L_∞-algebra structure comes naturally from the chain complex mentioned above. Further, the higher Lie bracket can be visualized geometrically. Finally, we will state the universality theorem: the natural morphism from the L_∞-algebra g of finite polygons to the directed Hochschild complex is a quasi-isomorphism. If time, we discuss the connection with Fukaya-Seidel categories.
主讲人简介
李龙飞, 现为美国堪萨斯州立大学博士生, 研究方向为同调镜像对称.
