My main interests lie somewhere between group theory, algebraic combinatorics and low dimensional topology (torus-like spaces for example). Precisely, I am into Artin-Tits braid groups (seen as fundamental groups or as purely algebraic structures) and the corresponding monoids, and I study them using the combinatorics of Coxeter groups and their fully commutative creatures. Sending topological stuff into Hecke-Temperley-Lieb algebras has given and is still giving us invariants. I am interested with the affine level...
Key words: Braid groups; Coxeter groups; fully commutative elements; Garside structure; Hecke algebras; Temperley-Lieb algebras; diagram algebras; Markov trace.