Jun Zhang (Online)
In this talk, we will introduce a new algebraic structure called triangulated persistence category (TPC) and discuss its associated K-theory. 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. 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 objects in the K-group of a derived Fukaya category from a quantitative perspective. This talk based on joint work with Paul Biran and Octav Cornea.