Title: Gigliola Staffilani: Dispersive PDEs and the I-Method"
In the early 2000's, Prof. Gigliola Staffilani (MIT) as well as Takaoka, Tao, Keel, and Colliander got to thinking about a rather fundamental question: Suppose I have global existence of some PDE emanating from some initial datum that's fairly regular-- when do I have global existence for (even slightly) less regular data? In this (introductory-ish) talk I will talk about what I mean by "regularity", what it means for a (dispersive) PDE to be well-posed, discuss the basics of global well-posedness, and then introduce the I-method: a technique designed to partially answer the above question. The overarching goal is to learn a little bit about both the fundamentals of dispersive PDEs, as well as an impressive result from a woman in mathematics.
