Homological Algebra for Persistence Modules

Explore the rich algebraic theory of persistence modules in this 55-minute lecture by Peter Bubenik. Delve into the world of homological algebra as it applies to persistent homology, where vector spaces are replaced by sequences of vector spaces and linear maps. Learn about key concepts such as tensor products and Hom operations between persistence modules. Discover how these operations produce new persistence modules and examine the challenges in preserving exact sequences when mapping between them. Gain insights into the joint work with Nikola Milicevic that addresses these complexities, offering a deeper understanding of the algebraic structures underlying persistent homology.