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.

Je joins ma voix à toutes celles qui dénoncent la barbarie de l’invasion russe en Ukraine.

latest news:
  • 13/05/22: We completely rewrote our paper with Yannick Guedes Bonthonneau on the marked length spectrum conjecture for manifolds with cusps, entitled Local rigidity of manifolds with hyperbolics cusps II. Nonlinear theory and just uploaded the new version to arXiv. There are major changes: first of all, we prove the expected theorem in full generality, that is, we show that the marked length spectrum locally determines the metric for cusp manifolds. Secondly, we clarify the exposition, especially the sections relative to the microlocal calculus tailored for cusp manifolds that we developed in the first paper Local rigidity of manifolds with hyperbolics cusps II. Linear theory and microlocal tools. Last but not least, the proof also relies on the meromorphic extension of the resolvent of the geodesic flow in Hölder-Zygmund regularity. Even for compact manifolds, and to the best of our knowledge, this was previously unknown. This should have interesting consequences, like some good regularity properties for SRB measures for instance.

A surface with three cusps. In red, a closed geodesic in a hyperbolic free homotopy class. In blue, a curve in a free homotopy class of loops wrapping once around a cusp: this class does not contain any closed geodesic.
  • 12/04/22: We just finished writing a short survey paper with Mihajlo Cekić, Andrei Moroianu and Uwe Semmelmann on frame flow ergodicity and, more generally, on ergodicity for certain isometric partially hyperbolic dynamics. Our aim was to explain the circle of ideas in our former paper unlocking Brin’s long-standing conjecture on the ergodicity of the frame flow on 1/4-pinched negatively-curved Riemannian manifolds. It is intended not to be too technical and also gives a broad overview of the historical context.
  • 07/04/22: We just uploaded our new paper with Mihajlo Cekić and Colin Guillarmou on local lens rigidity: we show that, on negatively-curved Riemannian manifolds with strictly convex boundary, the lens data, namely, the lengths of geodesics joining pairs of boundary points together with their incoming/outgoing vectors, locally determine the metric up to isometries. The proof is technical and based on Pollicott-Ruelle theory together with complex interpolation. The main obstacle to overcome is the lack of marking which makes this problem similar to the unmarked length spectrum rigidity on closed manifolds. This provides the first general result on lens rigidity with trapping in dimension greater than 2.