Dynamics and Complex Geometry

Head of the team : Pascale Roesch. Permanent members.

The team's activity can be summarized by the following key words: complex analysis of several variables, differential equations, foliations, classical algebraic geometry, complex analytic and algebraic geometry, discrete, continuous and symbolic dynamical systems, ergodic theory, singularities.

Here is a more detailed thematic spectrum:

Dynamical Systems, 2 main axes :

  • Differential equations and foliations : isomonodromic deformations ; classification of singuarities of curves and foliations ; singularities and bifurcations  ; Hamiltonian systems ; harmonic or stationary measures, Lyapunov exponents.

  • Discrete dynamics : holomorphic dynamics of one or several variables, artthmetic dynamics, Lyapunov exponents, chaotic dynamics, ergodic theory, with applications to combinatorics and number theory.

Complex Geometry, 2 main axes :

  • Existence of canonical metrics in Kähler or Sasaki geometry, as solutions of geometric PDEs of elliptic or parabolic type, with applications to classification problems in analytic or algebraic complex geometry ;

  • Study of compact complex varieties, from the projective to the non Kählér ones, including their geometry, their cohomologies, their deformations.

Interactions with other teams of the IMT :

  • Geometry, Topology, Algebra through complex algebraic geometry, differential Galois theory and dynamical systems of geometric origin ;

  • Analysis through analysis on manifolds, complex analysis, operator theory and calculus of variations ;

  • Probabilities through potential theory, orthogonal polynomials, large deviations theory and non-commutative analysis.

Team Life :

Mainly based on the two seminars Complex Geometry and Dynamical Systems, several working groups, and the team coffee C-Kawa.