Title: The associated primes of powers of ideals

Abstract: The goal of this talk is to introduce a result of Brodmann from the
1970s about the associated primes of powers of ideals. In particular,
Brodmann showed that for any ideal I in a Noetherian ring R, the set of associated primes of I^s, the s-th power of I, eventually stabilizes as s goes to infinity. I will discuss my own work on the associated primes of edge and cover ideals (monomial ideals related to graphs), and how the associated primes of the powers encode some information about the graph. I will review and introduce the all the needed commutative algebra and graph theory.