Primož Škraba (Queen Mary University), Moebius homology

Persistence diagrams are well studied invariants of filtrations, but there has been significant effort on generalizing them beyond filtrations to more general posets. There are many ways of defining persistence diagrams, which in the classic case all agree. In this talk, I will discuss the definition based on the Moebius inversion which is very amenable to generalization. Building on this, using poset topology we introduce a new invariant, which we call Moebius homology. This categorifies Moebius inversion and provides a surprising connection between Euler characteristics and persistence diagrams. Time permitting, a theorem on Galois connections and Moebius homology will be covered along with its applications to understanding the structure of this new invariant. This is joint work with Amit Patel.