Speaker:   Dr. Darren Glass, Gettysburg College.    

Abstract:   In this talk, we will introduce the notion of an arithmetical structure on a finite connected graph. These structures were defined by Dino Lorenzini in order to answer some questions in algebraic geometry, but in this talk we will discuss how they can be described only in terms of elementary number theory and linear algebra. One goal is to count how many different structures one can place on a given graph as well as discuss finite abelian groups that are associated to arithmetical structures. We will fully answer this question for some families of graphs, and discuss why it is a hard but interesting question for other families.