Peter Bubenik (10/28/20): Homological Algebra for Persistence Modules

Title: Homological Algebra for Persistence Modules

Abstract: In linear algebra, we work with vector spaces and linear maps. In persistent homology, we replace a vector space with a sequences of vector spaces and linear maps, called a persistence module. I will give an introduction to the rich algebraic theory of persistence modules. For example, one can multiply persistence modules (called a tensor product) and consider maps between persistence modules (called Hom) and both of these operations produce persistence modules! If we fix one of the inputs to these operations then we have a map from persistence modules to persistence modules. However, these mappings do not preserve exact sequences. Fixing this defect leads us to the wonderful world of homological algebra.

This is joint work with Nikola Milicevic.

Видео Peter Bubenik (10/28/20): Homological Algebra for Persistence Modules канала Applied Algebraic Topology Network