Geometry of Dimer Models

Explore the fascinating world of random dimer coverings in large planar graphs through this 55-minute lecture presented by Alexei Borodin from the Massachusetts Institute of Technology. Delve into the unusual asymptotic phenomena exhibited by these structures, including the formation of frozen regions and various phases in unfrozen areas. Focus on the Aztec diamonds, a specific family of subgraphs of the periodically weighted square lattice, and discover how their asymptotic behavior can be precisely described using the geometry of underlying Riemann surfaces. Gain insights into how the surface structure manifests itself through dimer statistics, based on joint works with T. Berggren and M. Duits. Recorded at IPAM's Vertex Models: Algebraic and Probabilistic Aspects of Universality Workshop, this talk offers a deep dive into the intersection of geometry, probability, and algebraic structures in dimer models.