报告人：于立（南京大学）  
邀请人：陈波
报告时间：2021年10月6日（星期三）10:00-12:00
报告地点：科技楼（南楼）713室
报告题目：Polyhedral Product的统一构造(II)
报告摘要：A panel structure on a topological space is just a locally finite family of closed subspaces. A space together with a panel structure is called a space with faces. In this talk, we introduce the notion of polyhedral product over a space with faces, which provides a unifying viewpoint on the constructions of polyhedral products and generalized moment-angle complexes in various settings.

We compute the stable decomposition of these spaces and use it to study their cohomology ring structures by the partial diagonal maps. Besides, we can compute the equivariant cohomology ring of the moment-angle complex over a space with faces with respect to some canonical torus action. The calculation leads to a notion of topological face ring of a space with faces, which generalizes the classical notion of face ring of a simplicial complex. We will see that many known results in the study of polyhedral products and moment-angle complexes can be reinterpreted from our general theorems on the polyhedral product over a space with faces. Moreover, we can derive some new results via our approach in some settings.

报告人简介：于立，副教授，硕士生导师，现任职于南京大学数学系。他主要从事代数拓扑学与几何拓扑学的研究，三项国家自然科学基金项目的主持人，另外入选江苏省“青蓝工程”优秀青年骨干教师计划。他的数学工作发表在Advances in Mathematics, International Mathematics Research Notices, Mathematical Research Letters, Algebraic and Geometric Topology等国际著名期刊上。他近几年的主要研究方向：带环面群作用的空间的拓扑与几何性质。