Periodic homogenization of diffuse interface models

I will discuss the periodic homogenization of diffuse interface energies and their L^2 gradient flows, or, in other words, the homogenization of Allen-Cahn-like equations with periodic coefficients. The main goal of the talk is to introduce the surface tension and the mobility, the two quantities that are expected to describe the homogenized behavior, and to explain what can be said about pulsating standing waves, which are so far the closest thing we have to correctors. Along the way, I will describe some particular examples that highlight pathologies that can occur.