A minisemester on the evolution of interfaces, Sapporo 2010
It is well-known that a precise analysis of evolving patterns and structures is not only mathematically interesting but also important for understanding complicated phenomena in science and technology. In this minisemester, we focus on surface evolution problems arising in materials science and image processing. Our goals are not only to solve mathematical problems but also to identify new mathematical questions and directions which will have impact on other disciplines. Therefore the minisemester will involve researchers with diverse backgrounds.
Singular diffusion arises naturally in both the evolution of crystals and the total variation flow. The former topic comes from materials science while the latter stems from image processing. Our understanding of these singular second-order diffusion problems has improved a lot in recent years, through analysis based for example on variational methods, viscosity solutions, and stochastic techniques. The purpose of this meeting is to clarify the state of the art, and to identify promising directions for further work. This event will gather mathematicians from various backgrounds who might not otherwise interact.