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Metric geometry on Grothendieck groups in symplectic geometry

组织者

范祐维

演讲者

Jun Zhang

时间

2024年04月10日 13:30 至 15:30

地点

A3-1-101

线上

Zoom 928 682 9093 (BIMSA)

摘要

In this talk, we will introduce a new method to carry out quantitative studies on the Grothendieck group of a derived Fukaya category. This fits into a bigger algebraic framework called triangulated persistence category (TPC). This category unites 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. In particular, 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 how to use this method to distinguish classes from the Grothendieck group (of a derived Fukaya category) from a quantitative perspective. This is based on joint work with Paul Biran and Octav Cornea.