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.