Braid groups

The mathematical notion of a braid was introduced in the formalisation of objects that model the intertwining of strings in three dimensions. The act of braiding strings is thus described by operators that can be composed to form algebraic structures known as braid groups. These groups naturally play an important role in knot theory and low-dimensional topology, but also in representation theory and mathematical physics. This project concerns the algebraic properties of braid groups, their quotients and generalisations thereof, the associated representation theories, and applications to Yang-Baxter integrable systems where the so-called Temperley-Lieb and BMW algebras are of particular interest