Graphs Viewed Through Commutative Algebra -
Edge ideals of graphs were introduced by Rafael Villarreal in the 1990s and binomial edge ideals were introduced by Herzog, Hibi, Hreinsdottir, Kahle and Rauh and independently by Ohtani, in 2010, all to study the graph-theoretic properties through commutative algebra.  The specific ideal-theoretic properties that play a role are various matching numbers, connectivity, the Castelnuovo-Mumford regularity,arithmetical rank, associated primes of powers of ideals, and more. This talk will be a survey of the area.