Castelnuovo-Mumford regularity of edge ideals of graphs (Siamak Yassemi, University of Tehran)

Let K be a field and S = K[x_1,…,x_n] be the polynomial ring in n variables over K. For a graded S-module M with minimal free resolution the Castelnuovo-Mumford regularity  is defined. We survey a number of recent studies of the Castelnuovo-Mumford regularity of the ideals related to a graph and their (symbolic) powers. Our focus is on the bounds and exact values for the regularity in terms of combinatorial data from associated graphs. This research program has produced many exciting results and, at the same time, opened many further interesting questions and conjectures.