A recent exciting development which bridges pure and applied mathematics and which has had a powerful and wide reaching effect involves new numerical and analytic techniques for computing geometric objects and capturing moving interfaces, as well as the real world applications (ranging from materials science to image processing) that can now be investigated using these new methods. The level set method and the theory of viscosity solutions have matured into enabling technologies. Related numerical and analytical ideas including high resolution numerical methods, convolution generated motion, threshold dynamics, dynamic surface extension, cellular automata, stochastic partial differential equations and harmonic maps, some of which are quite novel, some of which are classical, are relevant to Geometrically Based Motions.
The real applications of these and related ideas include: interfaces in materials science, computer aided design, robotics, high frequency wave propagation and inverse problems, e.g. in geophysics, image processing, computer vision, computer graphics, neuroscience, multiphase (reacting and non-reacting) flows in fluid dynamics, and the connection to structures. Other applications continue to arise.
The program will include workshops selected from the following topics: geometric flows, interfaces in geophysics, interfaces in material sciences, image processing with applications to neuroscience, computer vision, and computer graphics with applications to the entertainment industry. The goal of the program is to foster working relationships among researchers studying mathematical and numerical techniques and people doing real world applications.