Mini-Workshop: Three Facets of R-Matrices (hybrid meeting)

Abstract

By definition, an $R$-matrix with spectral parameter is a solution to the Yang-Baxter equation, introduced in the 1970's by C.N. Yang and R.J. Baxter. Such a matrix encodes the Boltzmann weights of a lattice model of statistical mechanics, and the Yang-Baxter equation appears naturally as a sufficient condition for its solvability.

In the last decade, several mathematical and physical theories have led to seemingly different constructions of $R$-matrices. The theme of this workshop was the interaction of three such approaches, each of which has independently proven to be valuable: the geometric, analytic and gauge-theoretic constructions of $R$-matrices. Its aim was to bring together leading experts and researchers from each school of thought, whose recent works have given novel interpretations to this nearly classical topic.