4:00 p.m., Monday (April 5th)
Princeton and Universite de Paris-Sud
Asymptotic shapes of crystalline surfaces
This is joint work with Andrei Okounkov. We study a simple model of
crystalline surfaces in R^3. These come from limits of discrete
interfaces in the dimer model (domino tiling model), and can be viewed
as a higher-dimensional generalization of the simple random walk,
where the domain is (part of) Z^2 instead of Z. We are interested
in the behavior of these interfaces in the scaling limit (limit
when the mesh tends to zero): the limit surfaces minimize a certain
surface tension functional which arises from purely entropic
considerations. Remarkably, the limit surfaces, which are solutions
of a nonlinear PDE, can be parametrized by analytic functions and
may contain facets in certain rational directions.
Refreshments will be served at 3:45 p.m. in the Faculty Lounge,
Math Annex (Room 1115).