Interface Fluctuations in Random Surface Models

Random surfaces are central paradigms in equilibrium statistical mechanics. As these surfaces become larger, their statistical behaviors become strongly dependent on how their boundaries are pinned down. This can lead to phase transitions, such as facet edges separating a flat region of the surface from the places where it curves. How do these surfaces look and fluctuate near such interfaces? The purpose of this talk is to explain some of these aspects, and to touch on some of the diverse mathematical concepts that go into its analysis.