New Strichartz estimates on tori and applications

I will start by reviewing the theory of Strichartz estimates, in particular the recent work of Bourgain and Demeter, who obtained optimal estimates on arbitrary tori for times O(1). Then I will show that better estimates, over longer time scales, become available for generic (irrational) tori. I will finally present some consequences for the nonlinear problem. This is joint work with Yu Deng and Larry Guth.