Perfect t-embeddings of Uniform Aztec Diamond Graphs

Explore a 45-minute conference talk on perfect t-embeddings of uniform Aztec diamond graphs presented by Matthew Nicoletti from the Massachusetts Institute of Technology at IPAM's Statistical Mechanics and Discrete Geometry Workshop. Delve into the concept of t-embeddings introduced by Chelkak, Laslier, and Russkikh, and their application in proving the convergence of dimer model height fluctuations to a Gaussian Free Field (GFF). Examine the properties of perfect t-embeddings of uniform Aztec diamond graphs, building upon the work of Chelkak and Ramassamy. Discover new exact formulas for t-embeddings derived from the integrability of the shuffling algorithm on these graphs. Gain insights into the precise asymptotic analysis of t-embeddings and its role in verifying technical assumptions required for GFF convergence. Conclude with a new proof of GFF fluctuations for the dimer model height function on the uniformly weighted Aztec diamond. Recorded on March 29, 2024, this talk offers a deep dive into advanced concepts in statistical mechanics and discrete geometry.