Thibault Lefeuvre

© Patrick Imbert, Collège de France

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 events:
latest news:
  • 19/01/23: With Jan Bohr and Gabriel Paternain, we have just uploaded on the arXiv our new paper on invariant distributions and the transport twistor space of closed surfaces. The purpose of this paper was twofold: first, to introduce the transport twistor space of a closed surface (following the approach of Bohr-Paternain for simple surfaces), which is a complex surface diffeomorphic to the unit ball bundle over the surface equipped with a \dbar operator degenerating to the generator of the geodesic flow on the boundary (the unit tangent bundle); second, to show that fiberwise holomorphic invariant distributions on the unit tangent bundle — which play a fundamental role in tensor tomography and solving the X-ray transform injectivity on the surface — correspond to traces of genuine holomorphic function on twistor space (in the same way as distributions on the real line are boundary values of holomorphic functions on the upper half-plane). This twistor space is a 2—1 branched cover over the (compactification of) the orientation compatible linear complex structures on the tangent bundle.
  • 18/01/23: We have just upoaded our new paper with Mihajlo Cekić, Andrei Moroianu and Uwe Semmelmann on the ergodicity of unitary frame flows on Kähler manifolds of negative sectional curvature and even complex dimension. This corresponds to the frame flow along geodesics restricted to frames compatible with the complex structure. In the same spirit of our first paper on frame flow ergodicity, we show that there is a holomorphic pinching (~0.9) such that pinched manifolds have an ergodic unitary frame flow. This extends results by Brin and Gromov.
  • 08/12/22: I am co-organizing with Mihajlo Cekić, Oana Ivanovici and Frédéric Naud the 2023 edition of the IMJ-PRG Summer School in Paris (July 2023). This year, the topic will be Microlocal and probabilistic methods in dynamics and geometry. There will be minicourses (by Colin Guillarmou, Malo Jézéquel, and Jared Wunsch) complemented by some research talks. Registration for the summer school just opened here! There will be a poster session for Ph.D students. If you want to present a poster, you can submit it to my email address.
  • 28/11/22: With Yann Chaubet, Yannick Guedes Bonthonneau and Leo Tzou, we just uploaded our new paper on the arXiv, in which we study geodesic Lévy flights and the narrow capture problem. Lévy flights are stochastic processes on Riemannian manifolds which, unlike Brownian motion, may jump from one point to another along geodesics. They are used in the field of biology to model predators hunting preys: this is known as the Lévy flight foraging hypothesis. We compute the asymptotics of the expected stopping time to find a small target the size of a geodesic ball of radius epsilon (as epsilon goes to zero) in a closed manifold. The proof relies on a precise analytic understanding of the generator of the pure jump Lévy process: we prove that, when the manifold is the sphere, the torus or has negative sectional curvature, it is an elliptic pseudodifferential operator.
  • 27/11/22: I will be giving the 2022-2023 Peccot Lectures in March 2023 on the topic: Dynamics and geometry in negative curvature: new progress and perspectives. I updated the webpage with the content of the course, see here (or tab « Enseignements »).
  • 07/11/22: I am very happy to announce that I was awarded the Brin Prize for Young Mathematicians for my work on dynamical systems at the 33rd Fall meeting of the workshop in dynamical systems at Penn State University! 🙂
  • 22/09/22: We finished writing our new paper with Mihajlo Cekić on polynomial structures over spheres. The paper is dedicated to the memory of Steve Zelditch who passed away on September 11th and was a leading figure in the field of spectral geometry to which this paper belongs. The aim of this article is to explain a relation between three a priori unrelated questions belonging to different fields:
    — In algebraic geometry: the classification of non-trivial polynomial maps between spheres,
    — In spectral theory: the study of isospectral connections (i.e. connections with same spectrum for their Bochner Laplacian), similarly to Kac’s original question for metrics Can one hear the shape of a drum?
    — In dynamical systems: the study of the ergodicity of certain partially hyperbolic flows obtained as isometric extensions over the geodesic flow in negative curvature.
    In particular, we show that, under a low-rank assumption, the spectrum of the Bochner Laplacian fully determines the connection and the topology of the underlying vector bundle.
  • 12/09/22: With Artur Avila and Mihajlo Cekić, I am co-organizing in May 2023 a workshop on Analytic techniques in dynamics and geometry in Les Diablerets (Swiss Alps). The website for the conference is here.