Pure Mathematics

  • Ordinary differential equations in the complex domain. Formal and analytic solutions. Stokes multipliers.

  • Formal and analytic solutions of partial differential equations.

  • Formal and analytic solutions of difference equations (including q-difference and differential-difference equations). Special functions (hypergeometric functions and others), orthogonal polynomials, continuous and discrete PainlevĂ© equations.

  • Integrable systems.

  • Holomorphic vector fields. Normal forms.

  • Asymptotic expansions, Borel summability.

  • Number theory, Analytical number theory, q-Calculus.

  • Schubert's Calculus, Intersection Theory.