**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.

Keywords

- 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.

Keywords

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.

Keywords

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.

Keywords

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.

Keywords

Birational geometry, Teichmüller space,

Complex and Differential Geometry

Functional inequalities

Metastability

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

##### Seminars

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

- The Geometry Seminar meets every week on Tuesdays in Tours,
- The C* working group meets regularly on Fridays in Orléans,
- The Analysis, Dynamics, and Geometry working group meets approximately once a month on Tuesday afternoons in Orléans,
- The Monthly Complex Dynamics Seminar takes place once a month on Fridays at the IHP in Paris.