BIMSA > Geometry and Dynamics Seminar Metric geometry on Grothendieck groups in symplectic geometry
Metric geometry on Grothendieck groups in symplectic geometry
Organizer
Yu Wei Fan
Speaker
Jun Zhang
Time
Wednesday, April 10, 2024 1:30 PM - 3:30 PM
Venue
A3-1-101
Online
Zoom 928 682 9093 (BIMSA)
Abstract
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.