Erik Duse: Dimer models

Abstract: In this talk I will show how to find the intrinsic conformal structure of the variational problem for dimer models. Moreover, I will introduce a natural class of domains and boundary values for the dimer models, and show how the conformal structure induces a strong rigidity of the liquid regions. In particular, this leads to a classification of the regularity of the liquid regions for all dimer models. Using this, I will discuss certain conjectures for the local boundary fluctuations. In a follow up talk on the analysis seminar April 25, I will discuss more of the analytical difficulties of the variational problem from a PDE perspective.