Directeur de Recherche
Section de Mathématiques
Centre National de la Recherche Scientifique (CNRS)

• Mathematical physics
  Properties of n-point functions in general quantum field theory.
  Exactly solvable quantum many-body systems (Calogero-Sutherland type).

• Groups and complex analysis
  Harmonic analysis in complex homogeneous spaces :
  Generalized Reinhardt domains, Hardy spaces, Cauchy and Poisson kernels.
  Generalization of the tube and three-circle theorems.

• Hermitian symmetric spaces
  Orbital structure, harmonic analysis, Hua equations, R-spaces.

• Jordan algebras
  Formally real and complex Jordan algebras :
  Inversible elements, Pierce decomposition.
  Quasi-invariant measures on the cone of squares.

• Algebraic combinatorics
  Symmetric functions, classical theory of partitions.
  Jack polynomials, Macdonald polynomials.
  Generalization of classical orthogonal polynomials (Hermite, Laguerre, Jacobi).
  Generalized binomial coefficients.
  Shifted Jack polynomials, shifted Macdonald polynomials.
  Characters of the symmetric group.

• Free probability theory

Back to top