AWM Emmy Noether Lecture
Abstract. Five ways in which crystals can grow (or shrink, or change their shapes) are discussed: motion by weighted mean curvature motion by surface diffusion motion by surface-attachment-limited kinetics with and without external driving forces, dendritic crystal growth, and motion of crystal aggregates in which individual crystals rotate. All are part of a family of motions which can be formulated and analyzed in the same general framework. Parts of this framework include a surface energy similar to that of soap bubbles (but varying with normal direction) and inner products determining the kinetics.