Untitled Document ABSTRACT: The interaction of mathematics and materials science has grown over the past twenty-five years into a major enterprise involving hundreds of mathematicians all over the world. A brief selective glimpse of the status of this activity in the year 2000 will be given, with an emphasis on the problems related to motion influenced by surface free energy. Specific topics to be addressed include motion by weighted mean curvature and by surface diffusion for single crystals and for polycrystalline materials. Some of the big open problems in the field will be outlined. Note; This is a repeat of the plenary talk given at the Mathematical Challenges meeting in August.
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