Title: Understanding the Interleaving Distances for Sheaves
Speaker: Justin Curry (Duke University)
Abstract: A version of the interleaving distance for (co)sheaves has been recently used by de Silva, Munch and Patel to define a novel distance on Reeb graphs, a classic tool in computer science. I will describe a new definition of the interleaving distance, which involves the push and pull operations of Grothendieck. Using the Vietoris-Mapping theorem, I will prove an obstruction-theoretic result: that two sheaves are infinite distance apart if their global sections are not isomorphic. This definition is inspired by the Radon transform on constructible functions in Euler calculus. I will point out how this distance induces a distance between certain group representations, as well.
Seminar URL: https://research.math.osu.edu/tgda/tgda-seminar.html