Triangulated persistence categories

This talk will discuss a new algebraic structure called triangulated persistence category (TPC). It combines the triangulated category structure with the persistence module structure. This algebraic structure can be used to associate a metric topology on the object-set of a triangulated category, which leads to various dynamical questions on a pure algebraic set-up. Many examples are naturally endowed with the TPC structure, for instance, derived Fukaya category, Tamarkin category, etc. In this talk, we will illustrate one algebraic example in depth via extending the Bondal-Kapranov’s classical pre-triangulated dg-category to a filtered version. This talk is based on an in-progress project joint with Paul Biran and Octav Cornea.