Abstract: Scaling limits of random tilings present surprising geometric features under suitable boundary conditions, and produce deterministic and disordered (also called frozen and liquid) limit configurations with interesting geometric properties.
This talk will show how via different methods from PDE's and the Beltrami equation in particular, one can understand the delicate geometry of the boundary between the deterministic/frozen and random/liquid phases. It turns out, for instance, that the geometry of the limit shapes within all dimer models is universal, i.e. independent of the specific model.
The talk is based on a joint work with E. Duse, I. Prause and X. Zhong.