Thibault Lefeuvre

I am a French mathematician, CNRS Junior researcher working at Sorbonne Université (IMJ-PRG), and former student of the Ecole polytechnique. I am also a writer, published by Gallimard. My first novel Éducation tropicale was published in 2018 and was awarded the Albert Bernard prize.

Upcoming talks:

Latest news:

  • 13/07/21: We just uploaded on the arXiv our new paper with Mihajlo Cekić on the generic injectivity of the X-ray transform. We show that the X-ray transform (namely, the operator of integration of symmetric tensors along closed geodesics) is generically injective on closed Anosov manifolds (i.e. manifolds with hyperbolic geodesic flow such as negatively-curved manifolds) and on certain manifolds with boundary and hyperbolic trapped set. Following earlier results by Guillarmou, Knieper and myself, this solves locally the marked length spectrum rigidity conjecture in a neighborhood of a generic Anosov metric. The proof is based on a perturbation theory of the zero eigenvalue of elliptic pseudodifferential operators that we develop: the basic strategy is to turn the problem of generic injectivity into an algebraic problem of representation theory by using Gaussian states.
  • 14/05/21: We uploaded yesterday on the arXiv our new paper with Mihajlo Cekić on the holonomy inverse problem. Given a negatively-curved Riemannian manifold, we consider the restriction of the Wilson loop operator of field theory to primitive closed geodesics. This operator, which we call the primitive trace map, consists in taking the trace of the holonomy of a unitary connection (on a certain vector bundle) along primitive closed geodesics. We conjecture that in odd dimensions > 2, the primitive trace map should be globally injective on the moduli space of all connections (up to gauge). We prove this result in a lot of situations: for almost-flat connections, for sums of connections on line bundles, and locally near a generic connection. The argument is based on two new ingredients: a Livsic-type theorem in hyperbolic dynamical systems, based on representation theory, showing that the cohomology class of a unitary cocycle is determined by its traces along closed geodesics, and a theorem relating the moduli space of connections and the Pollicott-Ruelle resonances near zero of a certain natural transport operator.
  • 14/05/21: We just uploaded on the arXiv a new version of our paper with Yannick Guedes Bonthonneau on radial source estimates in Hölder-Zygmund spaces for hyperbolic dynamics. The main consequence is that we can prove locally the marked length spectrum rigidity conjecture of Burns-Katok for metrics which are C^{3+}-close. As a byproduct, we also show that most of the known regularity results in hyperbolic dynamics (in particular those concerning Livsic theory) fit into this general framework of source-type estimates.