中科院数学与系统科学研究院
数学研究所
学术报告
拓扑研讨班
报告人:张俊(中科大)
题 目:Triangulated persistence category in symplectic geometry
时 间:2022.09.28(星期三)下午14:30-15:30
地 点: 腾讯会议:295-965-402
摘 要:In this talk, we will introduce a new algebraic structure called triangulated persistence category (TPC). A TPC combines the persistence module structure (from topological data analysis) and the classical triangulated structure so that a meaningful measurement, via cone decomposition, can be defined on the set of objects. Moreover, a TPC structure allows us to define non-trivial pseudo-metrics on its Grothendieck group, which is the first time that people can study a Grothendieck group in terms of the metric geometry. Finally, we will illustrate several unexpected properties of a TPC via its supporting example in symplectic geometry, the derived Fukaya category. In particular, we can distinguish classes in the Grothendieck group of a derived Fukaya category from a quantitative perspective. This is based on joint work with Paul Biran and Octav Cornea.