for this workshop
Mathematical questions in wave turbulence theory
American Institute of Mathematics, San Jose, California
Tristan Buckmaster, Pierre Germain, Zaher Hani, and Jalal Shatah
This workshop, sponsored by AIM and the NSF, will be devoted to mathematical questions in weak turbulence theory. This branch of equilibrium statistical physics tries to describe the dynamics of nonlinear waves over long time intervals, or in the presence of a random forcing. It was developed mostly by physicists and applied mathematicians in the past century, but very little is known rigorously in this field. It is our aim to advance its mathematical understanding.
The main topics for the workshop are
- Growth of Sobolev norms for nonlinear dispersive equations on compact domains.
- More generally, large time behavior of nonlinear dispersive equations on compact domains.
- Validity of the usual assumptions of weak turbulence theory (before all, phase independence)
- Derivation of the kinetic wave equation.
The workshop will differ from typical conferences in some regards. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.
The deadline to apply for support to participate in this workshop has passed.
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