Toric Ideals of Graphs

Abstract:

Toric ideals are a class of binomial ideals with many applications including to integer programming and algebraic statistics. One can associate a toric ideal to a finite simple graph by taking the kernel of the monomial map which sends the edges of the graph to the product of their endpoints. In this talk I will discuss some algebraic properties of toric ideals of graphs, focusing particularly on the Castelnuovo-Mumford regularity which is an invariant which measures the complexity of the relations among the generators of the ideal.