Abstract: |
The star-triangle relation is a distinguished form of the Yang-Baxter equation for two-dimensional exactly solved models of statistical mechanics. In recent times, the most general "master" solutions of the star-triangle relation have been discovered, which in addition to their application to exactly solved models, appear as important identities for elliptic hypergeometric integrals, supersymmetric gauge theory dualities, and classical multi-dimensionally consistent integrable systems. The first part of this talk will provide an overview of two-dimensional lattice models of statsitical mechanics, and the role the star-triangle relation plays for exact solvability, while the second part of this talk will present some of these more recent developments. |