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Workshop

Introductory Workshop in Nonlinear Dispersive Equations August 22, 2005 - August 26, 2005
Registration Deadline: August 10, 2005 almost 14 years ago
To apply for Funding you must register by: May 22, 2005 about 14 years ago
Parent Program:
Organizers James Colliander (Toronto), Patrick Gerard (Orsay), Herbert Koch (Dortmund), Natasha Pavlovic (Princeton), Daniel Tataru (Berkeley)
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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"
Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
Funding & Logistics Show All Collapse

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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.

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MSRI does not hire an outside company to make hotel reservations for our workshop participants, or share the names and email addresses of our participants with an outside party. If you are contacted by a business that claims to represent MSRI and offers to book a hotel room for you, it is likely a scam. Please do not accept their services.

MSRI has preferred rates at the Hotel Shattuck Plaza, depending on room availability. Guests can call the hotel's main line at 510-845-7300 and ask for the MSRI- Mathematical Science Research Institute discount. To book online visit this page (the MSRI rate will automatically be applied).

MSRI has preferred rates at the Graduate Berkeley, depending on room availability. Reservations may be made by calling 510-845-8981. When making reservations, guests must request the MSRI preferred rate. Enter in the Promo Code MSRI123 (this code is not case sensitive).

MSRI has preferred rates 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 "Affiliated with the Space Sciences Lab, Lawrence Hall of Science or MSRI." When prompted for your UC Contact/Host, please list Chris Marshall (coord@msri.org).

MSRI has a preferred rates at Easton Hall and Gibbs Hall, depending on room availability. Guests can call the Reservations line at 510-204-0732 and ask for the MSRI- Mathematical Science Research Inst. rate. To book online visit this page, select "Request a Reservation" choose the dates you would like to stay and enter the code MSRI (this code is not case sensitive).

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

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Schedule, Notes/Handouts & Videos
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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 (Osaka University)
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 (Université de Paris XI (Paris-Sud))
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 (University of California, San Diego)
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 (Université de Paris VI (Pierre et Marie Curie))