Geometry of the Doubly Periodic Aztec Dimer Model

Explore the geometry of the doubly periodic Aztec dimer model in this 50-minute conference talk presented by Tomas Berggren from the Massachusetts Institute of Technology at IPAM's Statistical Mechanics and Discrete Geometry Workshop. Delve into the complexities of the growing doubly periodic Aztec diamond dimer model, examining its arbitrary periodicity and edge weight conditions. Discover the three macroscopic regions - rough, smooth, and frozen - and learn how arctic curves, which form the boundaries between these regions, can be described using associated amoebas and action functions. Gain insights into the number of frozen and smooth regions, as well as the number of cusps on arctic curves. Investigate the convergence of local fluctuations to translation-invariant Gibbs measures in this joint work with Alexei Borodin, recorded on March 25, 2024, at the Institute for Pure & Applied Mathematics (IPAM) at UCLA.