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Geometric and Analytical Aspects of Nonlinear Dispersive Equations November 28, 2005 - December 02, 2005
Registration Deadline: November 21, 2005 over 17 years ago
To apply for Funding you must register by: August 28, 2005 almost 18 years ago
Parent Program:
Organizers Nicolas Burq, Hans Lindblad, Igor Rodnianski, Christopher Sogge, Sijue Wu

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This workshop is to be held at the International House on the UC Berkeley campus, at 2299 Piedmont Avenue. On site registration for the workshop will be at the International House, starting at 8:30 AM Monday and ending at 3:30 PM Monday. The field of nonlinear dispersive equations has experienced a striking evolution over the last fifteen years, gaining a place of its own within partial differential equations. During that time many new ideas and techniques emerged, enabling one to work on problems which until not long ago seemed untouchable. These include the systematic use of dispersive and Strichartz estimates for linear dispersive equations (used in the study of semilinear problems), the vector fields method for the linear and nonlinear wave equation, estimates for bilinear and multilinear wave interactions, the use of wave packet methods (for both linear and bilinear interactions), and the increasingly preeminent role played by the geometrical aspects of nonlinear dispersive equations. These ideas and methods have led to solutions to many problems. On the other hand, they have opened the way for the study of other unsolved problems, and in the process have spawned numerous open questions. It is difficult to predict where the field will be three years from now, but what is clear is that it is experiencing a very strong growth which is likely to continue for years to come. The evolution process for this field has its origin in two ways of quantitatively measuring dispersion. One comes from harmonic analysis, which is used to establish certain dispersive ($L^p$) estimates for solutions to linear equations. The second has geometrical roots, namely in the analysis of vector fields generating the Lorentz group associated to the linear wave equation. Ideas in harmonic analysis became even more important in the process of understanding the structure of nonlinearities, which is tied to the nonlinear wave interaction. Furthermore, there is now a two way interaction between harmonic analysis and the analysis of dispersive equations. Connections with number theory have also been established. On the other hand, one must also emphasize the geometrical aspects of these problems, which are slowly gaining a preeminent role in the theory. These arise in two ways. Many semilinear dispersive equations arise in geometrical contexts (e.g wave-maps, Yang-Mills) and the geometry of the target space for the solutions appears to determine certain properties of the equation. On the other hand, in both nonlinear problems and problems arising in nonflat geometries (e.g. on manifolds with various curvature properties) one needs to control the geometry of the underlying space-time and its effect on the corresponding equations. Geometry can also play a role in problems involving perturbations of ones in Minkowski space. For instance the presence or absence of trapped geodesics plays an important role in nonlinear equations involving obstacles or compactly supported metric perturbations. Geometry plays an important role in the study of nonlinear dispersive equations in several ways. One can begin with linear effects, caused by the geometry of the underlying space time. Sometimes one also needs to consider the geometry of the target space (manifold) which usually produces semilinear effects. Finally, the most difficult is the nonlinear case, where the geometry of the underlying space time itself depends on the solutions to the equation. While at this point we are far from having a good understanding of the geometric aspects of nonlinear dispersive equations, this is currently a hot topic and we anticipate that considerable progress will be made until the program begins. This workshop will bring together leading researchers in the field of nonlinear dispersive equations, especially ones whose work uses both analytic and geometric techniques. Its goal will be to follow several different threads, and introduce different problems and techniques to a wide spectrum of mathematicians. ----------------------------------- Preliminary Schedule of Speakers (updated 1 Nov. 2005) Monday, 11/28 9:30-9:45 Welcome to MSRI (at I-HOUSE) 9:45-10:45 A. Soffer: Dispersive Decay, Methods and Applications 11:00-12:00 C. Zeng: Energy estimates of free boundary problems of the Euler equation 12:00-2:00 Lunch Break 2:00-3:00 J.M. Delort: Almost global solutions for Hamiltonian Klein-Gordon equations on Zoll manifolds 3:00 -3:30 Tea Break 3:30-4:00 Travel to 60 Evans Hall, UCB 4:10-5:10 C. Kenig (at 60 Evans Hall, UCB): Some recent progress on the global well-posedness of dispersive equations Tuesday, 11/29 9:45-10:45 F. Planchon: Existence and uniquess for the Benjamin-Ono equation 11:00-12:00 L. Vega 12:00-2:00 Lunch Break 2:00-3:00 J. Shatah 3:00-3:30 Tea Break 3:30-4:30 S. Klainerman: A break-down criterion in General Relativity Wednesday, 11/30 9:45-10:45 X. Zhang 11:00-12:00 M. Weinstein 12:00-2:00 Lunch Break 2:00-3:00 M. Keel 3:00-3:30 Tea Break 3:30-4:30 J. Colliander Thursday, 12/01 9:45-10:45 J. Metcalfe: Elastic waves in exterior domains 11:00-12:00 H. Koch: Absence of positive eigenvalues for rough Schroedinger operators 12:00-2:00 Lunch Break 2:00-3:00 W. Craig: On the Boltzmann equation: global solutions in one dimensional geometry 3:00-3:30 Tea Break 3:30-4:30 T. Sideris: Incompressible elastodynamics Friday, 12/02 9:15-10:15 P. Raphael: Construction of a blow up solution for a L2 supercritical NLS equation 10:30-11:30 J. Sterbenz: Regularity for High Dimensional Gauge Fields ------------------------------------- This workshop will be held at International House Berkeley.
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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