Research interests

I used to consider myself a geometer, but now try to be a defi for labels. My main current interests are in dynamical systems and ergodic theory (expanding maps and thermodynamical formalism, Limit theorem, Markov chains), Riemannian geometry (isoperimetric inequalities, comparison geometry, minimal surfaces), and I work with tools such as linear programming (notably optimal transportation) and perturbation theory of linear operators.

Previously, I have worked on some Lie group actions (particularly on symmetric spaces of non-positive curvature), in CR and complex geometry, on the topology of spaces of subgroups and on geometric questions in optimal transportation.

Several other fields interest me, including functional analysis, probability theory, combinatorics and geometric measure theory.

Publications

All my research articles

A selection of papers of mine

[pdf]   Extensions with Shrinking Fibers.

[pdf]   Effective limit theorems for Markov chains with a spectral gap, to appear in the Annals of Applied Probability.

[pdf]   The calculus of the thermodynamical formalism joint with Paolo Giulietti, Artur O. Lopes and Diego Marcon Farias, to appear in Journal of the European Mathematical Society.

[pdf]   The Cartan-Hadamard conjecture and The Little Prince joint with Greg Kuperberg, to appear in Revista Matemática Iberoamericana.

[pdf]  The space of closed subgroups of Rn is stratified and simply connected, Journal of Topology 2 (2009).

Other recent preprints

[pdf]   An optimal transportation approach to the decay of correlations for non-uniformly expanding maps, to appear in Ergodic Theory and Dynamical Systems.

[pdf]   Empirical measures: regularity is a counter-curse to dimensionality
[Probablity theory]

[pdf]   Mixed sectional-Ricci curvature obstructions on tori with Stéphane Sabourau, to appear in Journal of Topology and Analysis.
[Riemannian geometry]

[pdf]   Effective high-temperature estimates for intermittent maps, to appear in Ergodic Theory and Dynamical Systems.
[Dynamical systems]

[pdf]   Effective perturbation theory for linear operators, to appear in Journal of Operator Theory.

By subject

Each keyword links to a list of relevant research papers, notes and expository papers.

Probability theory

Banach spaces

CR and complex geometry

Metric geometry

Riemannian Geometry

Lie groups and symmetric spaces

Isoperimetric inequalities

Dynamical systems

Geometric Ramsey theory

Chabauty topology

Optimal transportation

Economy and game theory

Memoirs

Miscellaneous

Various mathematical texts not meant to be published in peer reviewed journals.