# Mathematical Sciences Research Institute

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# Workshop

Introductory Workshop in Nonlinear Dispersive Equations August 22, 2005 - August 26, 2005
 Registration Deadline: August 10, 2005 over 8 years ago May 22, 2005 almost 9 years ago
Parent Program: Nonlinear Dispersive Equations
Organizers James Colliander (Toronto), Patrick Gerard (Orsay), Herbert Koch (Dortmund), Natasha Pavlovic (Princeton), Daniel Tataru (Berkeley)
Speaker(s)

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Description

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"

Funding & Logistics

## Show Funding

To apply for funding, you must register by the funding application deadline displayed above.

Students, recent Ph.D.'s, women, and members of underrepresented minorities are particularly encouraged to apply. Funding awards are typically made 6 weeks before the workshop begins. Requests received after the funding deadline are considered only if additional funds become available.

## Show Lodging

MSRI has preferred rates at the Rose Garden Inn, depending on room availability. Reservations may be made by calling 1-800-992-9005 OR directly on their website. Click on Corporate at the bottom of the screen and when prompted enter code MATH (this code is not case sensitive). By using this code a new calendar will appear and will show the MSRI rate on all room types available.

MSRI has preferred rates at the Hotel Durant. Reservations may be made by calling 1-800-238-7268. When making reservations, guests must request the MSRI preferred rate. If you are making your reservations on line, please go to this link and enter the promo/corporate code MSRI123. Our preferred rate is $129 per night for a Deluxe Queen/King, based on availability. MSRI has preferred rates of$149 - $189 plus tax at the Hotel Shattuck Plaza, depending on room availability. Guests can either call the hotel's main line at 510-845-7300 and ask for the MSRI- Mathematical Science Research Inst. discount; or go to www.hotelshattuckplaza.com and click Book Now. Once on the reservation page, click “Promo/Corporate Code“ and input the code: msri. MSRI has preferred rates of$110 - \$140 at the Berkeley Lab Guest House, depending on room availability. Reservations may be made by calling 510-495-8000 or directly on their website. Select “I am an individual traveler affiliated with MSRI”.

Additional lodging options may be found on our short term housing page.

## Show Visa/Immigration

Schedule
Aug 22, 2005
Monday
 09:15 AM - 10:15 AM Nonlinear Dispersive Equations-Lecture I Wilhelm Schlag 10:45 AM - 11:45 AM Wave Packet Methods for Hyperbolic Equations I Hart Smith (University of Washington) 02:00 PM - 03:00 PM Normal Forms in NLS Jean Bourgain (Institute for Advanced Study) 03:30 PM - 04:30 PM Nonlinear Dispersive Equations-Talk Gustavo Ponce (University of California, Santa Barbara)
Aug 23, 2005
Tuesday
 09:15 AM - 10:15 AM Nonlinear Dispersive Equations-Lecture II Wilhelm Schlag 10:45 AM - 11:45 AM Wave Packet Methods for Hyperbolic Equations II Hart Smith (University of Washington) 02:00 PM - 03:00 PM Nonlinear Dispersive Equations-Talk Kenji Nakanishi 03:30 PM - 04:30 PM Non-Generic Blow Up Solutions for the Critical Focusing NLS in1-d Joachim Krieger
Aug 24, 2005
Wednesday
 09:15 AM - 10:15 AM Strichartz Estimates for the Schrodinger Equation with Variable Coefficients Claude Zuily 10:45 AM - 11:45 AM Wave Packet Methods for Hyperbolic Equations III Hart Smith (University of Washington) 02:00 PM - 03:00 PM Nonlinear Dispersive Equations-Talk Ioan Bejenaru 03:30 PM - 04:30 PM Existence and Nonuniqueness for the Nonlinear Schrodinger Equation Michael Christ (University of California, Berkeley)
Aug 25, 2005
Thursday
 09:15 AM - 10:15 AM Dispersive Effects in High Rotating Fluids Jean-Yves Chemin 10:45 AM - 11:45 AM Nonlinear Dispersive Equations-Lecture III Wilhelm Schlag 02:00 PM - 03:00 PM Nonlinear Dispersive Equations-Talk Justin Holmer
Aug 26, 2005
Friday
 09:15 AM - 10:15 AM Well-Posedness of the Cauchy Problem for the mKdv Equation Yoshio Tsutsumi 10:45 AM - 11:45 AM Long-Time Existence for Semilinear Klein-Gordon Equations on Compact Manifolds Jeremie Szeftel (Universite Paris VI)