Mathematics Seminar - 08/28/26

Abstract: Arithmetical structures on graphs were introduced by Lorenzini in 1989 in the study of degenerating curves in algebraic geometry. Associated to an arithmetical structure is a finite Abelian group that arises is a number of contexts--the group of components in algebraic geometry, the sandpile group in statistical physics, the Smith group in linear algebra, and the critical group in chip firing. In recent years, arithmetical structures and their critical groups have been studied from a purely combinatorial perspective. This talk will discuss some of this work and its implications.