The Orlik-Solomon Algebra and its Representation Theory

The Orlik-Solomon algebra of a matroid is a combinatorially defined algebra that has a concrete topological interpretation. In this talk, we will discuss how the representation theory of the Orlik-Solomon algebra allows us to use combinatorics to compute important topological and geometric invariants of a matroid, as well as chip away at an open problem in number theory. A portion of the talk will discuss joint work with George Nasr, Nicholas Proudfoot, and Lorenzo Vecchi (arxiv link).