Speaker:

Robert MacPherson, Institute for Advanced Study

Title:

The Geometry of Grains

Abstract:

A metal or ceramic is naturally decomposed into cells called "grains".
The geometry of this cell complex influences the properties of the
material. Some interesting mathematical problems arise in trying to
understand the time evolution of these grains.  In 1952, von Neumann
gave a simple formula for the growth rate of a grain in 2 dimensions,
which has been used as the basis for much of the work on grain
evolution.  This formula will be generalized to 3 (and higher)
dimensions (joint work with David Srolovitz).  The generalization
relies on a good notion of the linear dimension of a 3 dimensional
grain called the "mean width", which should be useful in other
contexts.