# Condensed Matter seminar: "Grain Growth: materials, curvature flow, topology"

Grain growth is the process through which a polycrystalline material coarsens. Large grains grow, small grains shrink and disappear; the average grain size increases. This process is driven by the surface tension of the grain boundaries. The idealization of this is simply mean curvature flow on a cellular network. Beautiful exact results in 2d, derived by von Neumann and Mullins, take the problem from geometry to topology. Several years ago, we extended these results to all dimensions. Based on these exact results, we developed simulation methods to study the evolution of large polycrystalline networks. The key to understanding grain growth today is describing the evolution of the topology of these networks. I will present an approach to looking at the topology of such networks and discuss how topology provides clues to the evolution of the structure. I conclude by discussing the application of these new topological methods to condensed matter physics applications far from grain growth.