Dimers on a Riemann Surface and Compactified Free Field

Explore a 47-minute conference talk on dimers on Riemann surfaces and compactified free fields presented by Mikhail Basok from the University of Helsinki at IPAM's Statistical Mechanics and Discrete Geometry Workshop. Delve into the dimer model sampled on general Riemann surfaces, where the height function becomes additively multivalued with random monodromy. Examine the convergence of height functions to the compactified free field on the surface, building upon recent work by Berestycki, Laslier, and Ray. Discover Basok's contribution to this field, which provides an analytic description of the limit and identifies it with a version of the compactified free field. Learn about the application of discrete complex analysis to graphs embedded in locally flat Riemann surfaces with conical singularities. Gain insights into the regularity theory on t-embeddings developed by Chelkak, Laslier, and Russkikh, which forms a crucial part of this approach.