Workshop

The field of nonlinear dispersive equations has experienced a dramatic growth in recent years, and continues to evolve at a rapid pace. For the most part the problems which are being considered have their origin in physics in subjects such as general relativity, quantum mechanics, water waves, nonlinear elasticity, various field theories, etc. There is also a significant component which is tied to geometry. Even though most of the research so far is mostly theoretical, there is also a strong potential for applications as one moves from model problems towards the original equations. The key concept at the heart of the field is that of nonlinear wave interactions. These occur when waves, moving possibly with different speeds and in different directions, intersect. While in the linear theory such waves obey the principle of superposition, in nonlinear equations there is always some interaction. Initial research was concerned with interactions of small amplitude waves, which leads to small perturbations of linear regimes. However if the interaction is strong enough then it may create new waves or even lead to blow-up. The aim of the workshop is to provide an overview of the problems and methods in the field, and also to survey some of the recent developments. We plan to have two or three series of expository talks given by mathematicians who are leaders in the field, and to complement this with a number of more specialized one hour talks in targeted areas. Schedule Monday, Aug 22, 2005 9:00-9:15 MSRI Welcome 9:15-10:15 Wilhelm Schlag I 10:45-11:45 Hart Smith, "Wave packet methods for hyperbolic equations I" Lunch Break 2:00-3:00 Jean Bourgain, "Normal forms in NLS" 3:30-4:30 Gustavo Ponce Tuesday, Aug 23, 2005 9:15-10:15 Wilhelm Schlag II 10:45-11:45 Hart Smith, "Wave packet methods for hyperbolic equations II" Lunch 2:00-3:00 Kenji Nakanishi 3:30-4:30 Joachim Krieger, "Non-generic blow up solutions for the critical focusing NLS in 1-d" Wednesday, Aug 24, 2005 9:15-10:15 Claude Zuily, "Strichartz estimates for the Schrodinger equation with variable coefficients" 10:45-11:45 Hart Smith, "Wave packet methods for hyperbolic equations III" Lunch 2:00-3:00 Ioan Bejenaru 3:30-4:30 Michael Christ, "Existence and nonuniqueness for the nonlinear Schrodinger equation" Thursday, Aug 25, 2005 9:15-10:15 Jean-Yves Chemin, "Dispersive effects in high rotating fluids" 10:45-11:45 Wilhelm Schlag III Lunch 2:00-3:00 Justin Holmer Friday, Aug 26, 2005 9:15-10:15 Yoshio Tsutsumi, "Well-posedness of the Cauchy problem for the mKdV equation" 10:45-11:45 Jeremy Szeftel, "Long-time existence for semilinear Klein-Gordon equations on compact manifolds"