Keith Promislow is Professor of Mathematics at Michigan State. The material he will present in the winter school concerns the geometric evolution of structured interfaces.

Functionalized materials have embedded energy that drives the creation of interface, which is balanced against higher-order geometric effects such as curvature. Energy models for functionalized materials, based upon regularizations of the Canham--Helfrich energy, generate networks with bi-layer and pore-like morphologies.

Prof. Promislow will derive curvature driven flows for these structures which couple the geometric evolution to the intrinsic parameters of the structures.