Liliana Borcea (University of Michigan) will present "The Dirichlet to Neumann map of high contrast media." Abstract: I will describe a problem of electrical conduction in a composite material consisting of highly conducting inclusions packed close together so they are close to touching. The mathematical model is an elliptic equation in divergence form, with a high contrast coefficient. I will describe the homogenization problem for this equation, but the goal is to get more detailed information in order to approximate the Dirichlet to Neumann map. I will show how to obtain such an approximation using variational principles and asymptotic analysis.