SPECIAL LECTURE: Differential calculus for modules over posets
Lecturer: Ran Levi | University of Aberdeen

Abstract:

The motivation for this project arises from topological data analysis. The concept of a persistence module was introduced in the context of topological data analysis. In its general form one defines persistence modules as functors from an arbitrary poset (or more generally an arbitrary small category) to some abelian target category. In other words, a persistence module is simply a representation of the source category in the target abelian category. As such much research was dedicated to studying persistence modules in this context. Unsurprisingly, it turns out that when the source category is more general than a linear order, then its representation type is generally wild. In particular, keeping in mind that persistence module theory is supposed to be applicable, computability of general persistence modules is very limited. In this talk I will describe a new set of ideas for local analysis of modules over poset algebras by methods borrowed from spectral graph theory and multivariable calculus.