Tuesday, February 2
9:00-9:30, 330 Phillips Hall    Refreshments
9:30-10:30, 208 Phillips Hall    Patrick Gerard, Lecture 1: Introduction to long time estimates
10:30-11:00, 330 Phillips Hall    Tea
11:00-12:00, 328 Phillips Hall    Joseph Thirouin: Long time estimates for fractional Schroedinger equations on the circle

Wednesday, February 3
9:30-10:00, 330 Phillips Hall    Tea
10:00-11:00, 247 Phillips Hall    Patrick Gerard, Lecture 2: The cubic Szegö equation on the circle and its special structure

Thursday, February 4
10:30-11:00, 330 Phillips Hall    Tea
11:00-12:00, 220 Peabody Hall    Patrick Gerard, Lecture 3: Long time transition to high frequencies

Abstracts:

Patrick Gerard, Long time estimates of solutions to Hamiltonian nonlinear PDEs:

This minicourse is devoted to long time behavior of solutions to nonlinear PDE’s such as nonlinear Schroedinger equation or nonlinear wave equations. More precisely, we would like to provide an introduction to the following general question, closely connected to wave turbulence: assume that such a nonlinear PDE is globally well-posed on high regularity Sobolev spaces; how big can the high Sobolev norms be of generic solutions as time goes to infinity? The second part of the course will be focused on the special case of the cubic Szegö equation, which is a model of a nonlinear wave evolution and enjoys some integrable structure allowing to study its solutions in detail.