Coxeter groups

The theory of Coxeter groups provides a common framework for important classes of groups such as symmetric groups, Weyl groups, reflections groups (finite, affine, hyperbolic) and symmetry groups of regular polytopes. These objects are central in Lie theory, algebraic geometry and combinatorial geometry among other subjects. We shall study Coxeter groups using mainly combinatorial techniques, although connections with other areas will be prevalent. This is a thriving field of research, and we shall touch upon very recent results on several occasions.