Dynamics in Geometric Dispersive Equations and the Effects of Trapping, Scattering and Weak Turbulence (14w5080)


Stephen Gustafson (University of British Columbia)

(University of North Carolina)

Daniel Tataru (UC Berkeley)


The Banff International Research Station will host the "Dynamics in Geometric Dispersive Equations and the Effects of Trapping, Scattering and Weak Turbulence" workshop from May 4th to May 9th, 2014.

The advances and methods of late in the mathematical analysis of General Relativity, Schroedinger/Wave Maps, Nonlinear Bound States, Water Waves, Optics, and the evolution of dispersive equations on curved surfaces, have been quite rapid. Often, as a result, there are links to open problems, related questions and applications of techniques that may go unnoticed in other related fields. We plan to bring together a number of mathematicians working in geometric analysis, dynamical systems and dispersive equations with overlapping interests related to mathematical models on spaces with curvature, boundary, obstacles, or other possible obstructions to dispersion.

Geometry has taken a larger and larger role in areas of mathematical physics as analytical techniques become more and more advanced to deal with the complexity of nonlinear equations on non-flat background geometries. In some cases, such as general relativity and electromagnetism, the geometry plays a major role in the underlying theory. In other cases such as optics, generalizing the equations geometrically can give insight into how well the model equations work on finite systems, and clarify whether any new physics can be discovered in more complex models. While many mathematicians are working in these areas, often they tend to work on specialized equations and hence rarely have the opportunity to come together and learn about other related topics in analysis where advances could be made or techniques shared and/or modified through collaboration and communication.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT).