In this talk, we will introduce a new algebraic structure called triangulated persistence category (TPC). A TPC combines the persistence module and the classical triangulated structure so that a meaningful measurement, via cone decomposition, can be defined on the set of objects. We will also elaborate on various examples of TPC that come from algebra, topology, and symplectic geometry. Finally, we will investigate the Grothendieck group of a TPC and explain several unexpected properties. This talk is based on joint work with Paul Biran and Octav Cornea.
This video is part of the New Directions in Group Theory and Triangulated Categories seminar series.
