Will Feldman: Shapes of equilibrium capillary drops on a rough surface
I will discuss some simplified models for the shape of liquid droplets on rough solid surfaces. These are elliptic free boundary problems with oscillatory coefficients. I will talk about the large scale effects of small scale surface roughness, e.g. contact line pinning, hysteresis, and formation of flat parts (facets) in the contact line, and how to understand these by homogenization theory. I will also mention a connection with the continuum scaling limit of an abelian-sandpile-type model and some results in that setting.