Triangulated Persistence Categories and Their K-Theory

Explore the concept of Triangulated Persistence Categories (TPC's) in this 55-minute lecture presented by Paul Biran for the Applied Algebraic Topology Network. Delve into the fusion of triangulated category theory and persistence module theory, uncovering the resulting measurements and invariants. Gain insights into the K-theory associated with TPC's and examine its applications in both algebraic categories, such as the homotopy category of filtered chain complexes, and geometric situations, specifically the filtered Fukaya category from symplectic topology. Based on collaborative research with O. Cornea and J. Zhang, this talk offers a comprehensive overview of TPC's and their significance in advanced mathematical studies.