Sheaves as Topological Descriptors of Datasets

Ever wondered why I keep talking about sheaves while being part of the “applied” side of the group ? In this talk, I will explain how (derived) sheaf theory (after Kashiwara-Schapira) can be used as a theoretical foundation for persistence theory (the algebraic theory associated to most Topological Data Analysis constructions). If time permits, I will also explain how taking this point of view allows to define new computable topological descriptors of datasets using…derived Grothendieck operations!