## What we do

The main areas of research in our group are:

- algebraic combinatorics
- quantum groups
- algorithmic aspects of algebraic curves
- geometric group theory
- homological algebra
- combinatorial and geometric semigroup theory
- automata and languages
- knot theory and 3-manifolds
- noncommutative geometry
- differential, complex and algebraic geometry
- K-theory
- higher algebraic and geometric structures such as n-Lie algebras and higher Poisson structures
- moduli spaces for elliptic PDE's

We have close links with the Geometry and Mathematical Physics research groups within the Maxwell Institute.