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)   

 Triangulated persistence category in symplectic geometry

  2022.09.28(星期三)下午14:30-15:30

 点: 腾讯会议:295-965-402

  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.

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