Integrability and Representation Theory Seminar: Perfect t-embeddings of Hexagon
- Event Type
- Seminar/Symposium
- Sponsor
- IRT Seminar
- Location
- AH 343
- Date
- Feb 27, 2025 1:00 pm
- Speaker
- Marianna Russkikh
- Contact
- Trung Vu
- hvu@illinois.edu
- Views
- 21
- Originating Calendar
- Integrability & Representation Theory (IRT) Seminar
A new type of graph embedding called a (perfect) t-embedding, was recently introduced and used to prove the convergence of dimer model height fluctuations to a Gaussian Free Field (GFF) in a naturally associated metric, under certain technical assumptions. We will describe a construction of perfect t-embeddings for regular hexagons of the hexagonal lattice and discuss their properties. The construction provides the first example, and hence proves the existence of perfect-t-embeddings for graphs with an outer face of a degree greater than four. As a consequence, this construction leads to a new proof of GFF fluctuations for the dimer model height function on uniformly weighted hexagon.