Christian Serio

My research focuses on probability theory and its applications to statistical mechanics. I am especially interested in understanding universal scaling limits of random interface models.

Random interface models are used in statistical mechanics and mathematical physics to describe the separation of different phases in a physical system. A concrete example is the shape of a droplet of liquid condensing onto a solid. Many such models, although seemingly different from one another microscopically, are expected to display common “universal” large-scale behavior described by the Kardar–Parisi–Zhang (KPZ) universality class. It is a major open problem in mathematics to give a rigorous and complete description of this universality class. Some of my recent work has focused on understanding the geometry of random surfaces through the lens of objects known as Gibbs line ensembles. Roughly, these are collections of random interacting curves, which can describe the contour lines of a two-dimensional surface. By developing probabilistic techniques to analyze these ensembles, my collaborators and I have proven results describing universal KPZ-type limiting behavior of various random interface models, including models describing crystal growth and ferromagnetism.