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Accueil > Research teams > Analyse > Research themes

Research themes    fr

The main themes of research in our team are

- various aspects of the theory of ordinary differential equations, difference equations and other functional equations (Thomas Dreyfus, Frédéric Fauvet, Viktoria Heu, Loïc Jean-dit-Teyssier, Claude Mitschi, Reinhard Schäfke)
- theory of holomorphic and sub-harmonic functions of one and several variables (Myriam Ounaies, Raphaële Supper), harmonic analysis, theory of dynamical systems in relation with partial differential equations (Nalini Anantharaman)

More precisely, the current research themes are concerning

- analytic and geometric properties of differential equations with holomorphic coefficients: search for normal forms, classification of foliations, Riemann-Hilbert problems, isomonodromic deformations and monodromy evolving deformations, Painlevé equations, moduli spaces
- summability of divergent series, resurgent functions and their applications to certain functional equations
- singularly perturbed ordinary differential equations (existence and approximation of solutions)
- o-minimal structures generated by the solutions of irregular singular equations
- differential Galois theory
- sub-harmonic functions, Riesz measure, Bloch-type growth
- entire functions with exponential growth, conditions for uniqueness, zero-set, interpolation
- Dirichlet-series, inequality of Bohnenblust-Hille
- hyperbolic dynamical systems, spectral theory of hyperbolic manifolds
- Schrödinger equation on Riemannian manifolds, quantum chaos
- harmonic analysis on graphs
- generating series of walks in the quarter plane.