This award supports travel for US participants in the "Tenth International Conference on Mathematical and Numerical Aspects of Waves (Waves 2011)," held 25-29 July 2011 at the Simon Fraser University Vancouver campus, BC, Canada. The meeting focuses on mathematical developments in the theory of wave propagation and its applications. Themes for the meeting include forward and inverse scattering, fast computational techniques, approximate boundary conditions, domain decomposition, nonlinear wave phenomena, water waves and coastal modeling, guided waves and random media, and medical and seismic imaging.

The meeting is a satellite conference of the International Congress on Industrial and Applied Mathematics (ICIAM 2011), held in Vancouver the preceding week.

In addition to invited talks, the meeting includes invited minisymposia, a poster session to showcase student achievements, tutorial lectures for graduate students, and an "Industry Meet-and-Greet" to enhance interactions between academic researchers and representatives from interested companies. The conference encourages and supports participation by graduate students, junior researchers, and members of under-represented groups.

Conference web site:

Project Report

This NSF supported grant was instrumental in supporting graduate students and postdoctoral fellows for the WAVES 2011 conference held in Vancouver, BC in July 2011. The conference series is built around the mathematical and computational investigation of waves propagating in a medium with inhomogeneities. The waves of interest may describe elastic, electromagnetic, pressure or acoustic fields. The setting for these waves cover a gamut of applications, e.g. radar, water and atmospheric waves, waveguides, non-invasive medical imaging, seismic exploration and each scenario presents its own particular set of challenges. Mathematically, however, there are substantial commonalities among wave propagation problems, so that progress made in one application usually leads to breakthroughs for other, seemingly unrelated, problems. Increasingly complex physical systems (e.g.,where material properties vary or where several spatial and temporal scales are involved) are relevant forengineering and biomedical applications. Though the application areas of wave propagation are incredibly diverse, many underlying mathematical issues inherent in the analysis and simulation of wave propagation processes are common. Despite the outwardly simple appearance of the governing equations, their solution raises very difficult mathematical questions - what is the underlying regularity of solutions? What is the effect of computational approximations on stability and well-posedness? To address these issues, researchers rely on a wide array of mathematical techniques, including approximation theory, analysis, PDE theory, asymptotics, and the interplay between these. These mathematical insights are then translated into computational strategies. Clearly, broad progress at a mathematical level translates into computational benefits in many fields. To date, these efforts have been so successful that complex three-dimensional simulations which once necessitated the use of the world's most advanced supercomputers can now be realized on desktop computers. However, as technological advances in novel materials and devices continue, the frontiers of existing algorithms are being pushed, and an injection of new mathematical ideas becomes vital. The WAVES conference series is a key venue where updates in this field are disseminated, and a concerted effort to identify commonalities in research areas is made. New applications and ideas are brought to the community and cross-fertilization is strongly encouraged. The close collaboration of mathematical theorists with physical scientists, engineers, and medical professionals that this grant fostered will potentially significantly broaden and enhance the students' educational experiencesand prepare them for a range of future opportunities, ultimately enhancing the mathematical workforce of the 21st century. The combination of ubiquitous wave phenomenon, their complex interactions, and uncertainty underlying many of the fundamental open problems in waves is spurring the development of advanced computational and analytic and technological innovations. Therefore, beyond the specific training and research that it will produce in applied mathematics, the research efforts will contribute to vitality and evolution at the core of mathematics in modern wave theory and computation.

National Science Foundation (NSF)
Division of Mathematical Sciences (DMS)
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Henry A. Warchall
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University of Washington
United States
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