We are interested in relations between algebra and combinatorics, with the aim of producing efficient algorithms in the following domains:
> Combinatorics of the symmetric group, Hecke algebras and Young tableaux and its applications to the representations of classical and quantum groups.
> Symmetric functions.
> Non-commutative determinants.
> Schubert and Grothendieck polynomials, geometry of flag varieties.
> Lie groups and Lie algebras.
> Combinatorial Hopf algebras.
> Invariant theory and quantum information.