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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.