Geometry of Dimer Models - ICBS 2024

Explore the fascinating world of random dimer coverings in large planar graphs through this 1-hour 3-minute lecture by Alexei Borodin at ICBS2024. Delve into the unusual asymptotic phenomena exhibited by these coverings, including the formation of frozen regions and various phases in unfrozen areas. Focus on the Aztec diamonds, a specific family of subgraphs within the periodically weighted square lattice, and discover how their asymptotic behavior can be precisely described using the geometry of underlying Riemann surfaces. Learn how the surface structure manifests itself through dimer statistics, drawing from joint works with T. Berggren and M. Duits. Gain valuable insights into this complex mathematical topic and its visual representations in planar graphs.