Braid Groups can arise naturally in a number of different ways. Intuitively one may view braid groups as 'strands' between some finite sets of points with some naturally defined composition. More formally, one can define braid groups as the fundamental group of some configuration spaces. In turn, these are isomorphic to the mapping class group of the n-punctured disc.

In tonight's discussion group Paul Mortimer will give an introduction to braid groups along with what he covered in his project. This talk may unfortunately not be for the faint hearted. The material was described to us by Paul as "PhD level". He did go on to clarify, "the most difficult aspect of the project was presenting it in a fashion understandable to fellow fourth years." There is therefore some hope that the talk will be an understandable account of Paul's wonderful achievements over the past two terms. Stay Categorical!

Two major areas of combinatorics are enumeration (counting), and graph theory (drawing): in this presentation, we hope to guide the audience through the art of enumerative graph theory (counting what you have drawn). In particular we will look at enumerating spanning trees of graphs, a problem which can be tackled from numerous directions, showcasing many of the combinatorists favourite weapons. Finally we will see some applications of such enumeration in other areas. The presenter is prefers projects involving (easy) problem solving rather than exposition, so the talk should be followable by all.

So join Owen Daniel, and his graphs of many shapes and sizes on Monday night, before we follow a Hamiltonian path to the pub...