BIMSA-YMSC Geometry and Dynamics Seminar | Metric geometry on Grothendieck groups in symplectic geometry

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.

Speaker

I am working on Symplectic Topology. My research interests include Hamiltonian dynamics, Floer theory, topological data analysis, and microlocal sheaf theory. More explicitly, I have been studying symplectic and contact geometric objects from various quantitative perspectives and creating new symplectic and contact invariants.