Minimal Bipartite Dimers and Maximal Riemann Surfaces

Explore a 52-minute lecture on minimal bipartite dimers and maximal Riemann surfaces presented by Cédric Boutillier from Sorbonne Université at IPAM's Statistical Mechanics and Discrete Geometry Workshop. Delve into the extension of Richard Kenyon's 2002 work on critical weights for dimers on isoradial graphs. Examine the results of collaborative research with Béatrice de Tilière and David Cimasoni, focusing on a broader family of weights. Discover how Kasteleyn matrices constructed from theta functions on maximal Riemann surfaces, using Vladimir Fock's formula, yield a two-dimensional family of inverses with explicit integral representation and locality properties. Investigate applications to the Kenyon-Okounkov spectral theorem and Laplacians on isoradial graphs. Recorded on March 28, 2024, at the Institute for Pure & Applied Mathematics (IPAM) at UCLA, this talk offers insights into advanced concepts in statistical mechanics and discrete geometry.