Nonlinear Water Waves: Rigorous Analysis and Scientific Computing (24w5207)

The Banff International Research Station will host the “Nonlinear Water Waves: Rigorous Analysis and Scientific Computing” workshop in Banff from October 27 - November 1, 2024.

Water waves (that is, waves on the surface of a fluid, or the interface between different fluids) have been seen by everyone, and are naturally physically fascinating. However, as Richard Feynman wrote in his lecture, water waves that are easily seen by everyone, and which are usually used as an example of waves in elementary courses, are the worst possible example; they have all the complications that waves can have. In this sense water waves are a paradigm for problems in mathematics, physics and numerical simulation.

The last few years have seen an explosion in research activity in mathematics and computing for water waves, to the extent that previously intractable issues such as large waves, waves with vorticity (local rotation effects) and ocean waves can now be mathematically described and simulated on computers. There have been research programmes at leading mathematical institutes around the world, workshops at major conferences and an explosion in the numbers of highly talented early career researchers. It thus appears timely to convene a further workshop in Banff to review the state of the art (including in particular a number of recent unexpected breakthroughs using methods from apparently unconnected areas of mathematics). The workshop will distinguish itself from other events by concentrating on the interaction between researchers with expertise on rigorous mathematical analysis and experts on scientific computing for the exact hydrodynamic equations, bridging the divide between Pure and Applied Mathematics.

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).