Daniel Katz

Let (R,m) be a quasi-unmixed local ring. The celebrated Rees multiplicity theorem states that if J and I are m primary ideals, with J contained in I, then J is a reduction of I if and only if J and I have the same multiplicity. This theorem has been generalized in a number of ways over the years by numerous authors, including Rees himself. The purpose of this talk is to give a survey of some of these generalizations, including some recent variations by Flenner-Manaresi and Katz-Trung.