Algebra from Statistical Mechanics

In this talk I will give a pedagogical introduction to lattice models in statistical mechanics with a particular focus on algebraic techniques for computation. The main protagonist in this story is the transfer matrix which provides a computational formalism amenable to a mathematical deconstruction. We will see that the transfer matrix can be constructed from an underlying algebra, whereby a connection with certain objects studied by algebraists today such as Temperley-Lieb algebras and Hecke algebras, is revealed. Time permitting, we will discuss the physical significance of the representation theory of these algebras.