Asymptotic colengths for families of ideals

In this talk we discuss the existence and the importance of asymptotic colengths for families of m-primary ideals in a Noetherian local ring (R,m).  We explore various families such as weakly graded families, weakly p-families and weakly inverse p-families. If time permits we discuss the new analytic method to prove the existence of limits. This talk is based on a joint work with Cheng Meng.