Maru Sarazola, University of Minnesota
 
A homotopical framework for path homology of directed graphs

Tuesday, Nov 14th, 11:00am

Abstract: Traditionally, the way we compare mathematical structures is by using the notion of equality, or even of isomorphism. However, there are many settings where this is no longer the natural notion of "sameness". A notable example occurs when our objects admit a homology construction: then, we want two objects to be "the same" if they have identical homology. Homotopy theory provides the framework required to work in these settings. In this talk, we will describe an algebraic invariant of directed graphs called "path homology", and introduce a new homotopical framework that encodes "sameness up to path homology". We will also show how this new framework allows us to make homology-invariant constructions.