Karen Smith

Abstract:   In recent years, there have been a flurry of questions about uniform behavior in commutative algebra and algebraic geometry. In this talk, I will try to give a feeling for this type of inquiry by presenting five rather different looking such questions. These questions are unified in that they all have been solved or approached using multiplier ideals. Multiplier ideals can be defined in three ways. Originally defined by analysts, are functions in some L2-space. For algebraic geometers, they are defined via resolutions of singularities. For commutative algebraists, they are defined in rings of prime characteristic using tight closure. In this talk, I will discuss a few of the diverse problems about uniform behavior in algebra and geometry that have been solved using multiplier ideals, as well as the different perspectives from which multiplier ideals can be viewed.