Equipe d’Analyse et Géométrie

Team animators : Julie Déserti (Orléans) & Romain Gicquaud (Tours)

The topics addressed within the team span a wide spectrum from Geometry to PDEs: Operators algebras and Functional analysis, Complex Analysis and Dynamical Systems, Harmonic Analysis, PDEs, Spectral Theory and Geometry.

Operator Algebras and Functional Analysis

It encompasses works on K-theory and the Baum-Connes conjecture, as well as connections between C*-algebras and dynamical systems, representation theory of groups, group actions, or dynamics of complex foliations.


  • C*-algebras and dynamical systems
  • C*-algebras and group representations
  • K-Theory, Baum-Connes conjecture, and group representations
  • Group actions, group theory, geometry, and topology
  • JBW*-triplets as Banach spaces
Complex analysis and Dynamical Systems

The team members are interested in discrete dynamical systems with one or more complex variables generated by a family of transformations, growth processes, and their potential applications.


Holomorphic dynamics, bifurcations
Birational transformations dynamics
Random dynamical systems
Growth processes and applications

Harmonic Analysis

The questions surrounding harmonic analysis involve work on spaces with non-positive curvature, Hardy spaces, and the exploitation of the dispersive properties of certain partial differential equations for their study.


Harmonic analysis, Hardy spaces, spaces with non-positive curvature
Harmonic analysis and PDEs
Potential and pluripotential theory
Applied harmonic analysis: Modeling of diffusion in porous media with temperature gradient

Partial Derivative Equations

Different types of considerations surrounding various types of partial differential equations are addressed: degenerate elliptic equations, fractional diffusion equations in time, the Keller-Segel model, inverse problems, observability problems, and quantum limit problems.


Keller-Segel model
Inverse problems for PDEs
Fractional diffusion equations in time
Degenerate elliptic equations
Observability and quantum limits

Spectral Theory and Geometry

Geometry is to be understood here in a very broad sense, as it may involve birational geometry, spectral geometry with singularities or sub-Riemannian geometry, minimal surfaces, analysis on manifolds, as well as knot theory, the study of geometric equations on hyperbolic space, or problems related to general relativity.

The spectral theory problems studied within the institute include metastability problems, quantum Hamiltonians.


Birational geometry, Teichmüller space,
Complex and Differential Geometry
Functional inequalities
Spectral geometry with singularities, Sub-Riemannian spectral geometry
Minimal surfaces and constant mean curvature surfaces
Knot theory
Initial data in general relativity
Geometric equations on hyperbolic space


The team members structure their work around seminars or working groups that they organize: