Wojciech Chachólski - TDA Invariants and Model Categories

Explore the intersection of data analysis and homotopy theory in this 54-minute lecture by Wojciech Chachólski. Delve into the balancing act of simplification and information retention in data analysis, drawing parallels with homotopy theory's core principles. Learn about (co)localisation techniques from homotopy theory and their application in extracting simplifying invariants. Discover how approximating complex objects with simpler, more manageable ones, such as cofibrant objects in a model category, can lead to effective data simplification. Examine the category of tame persistent chain complexes over a field and its model structure, which offers a simple decomposition theorem for indecomposable cofibrant objects. Gain insights into weak equivalences, approximations, and contractible spaces as part of the modified persistent pipeline in data analysis. This lecture, part of a two-seminar series, introduces these advanced concepts to a general audience, setting the stage for practical applications discussed in the subsequent seminar.