Publications

Semiclassical analysis of the magnetic Laplacian on hyperbolic surfaces, to appear in the Proc. Journées Equations aux Dérivées Partielles [PDF]
The Pestov identity on the frame bundle and associated homogeneous fibrations, with Mihajlo Cekić, Andrei Moroianu and Uwe Semmelmann [PDF]
Marked Poincaré rigidity near hyperbolic metrics and injectivity of the Lichnerowicz Laplacian in dimension 3, with Karen Butt, Alena Erchenko, Tristan Humbert, and Amie Wilkinson [PDF]

Books

Microlocal Analysis in Hyperbolic Dynamics and Geometry, Cours spécialisés de la SMF (32), 2025

Semiclassical analysis, quantum ergodicity

Semiclassical defect measures of magnetic Laplacians on hyperbolic surfaces, with Laurent Charles [PDF]
Semiclassical analysis on principal bundles, with Mihajlo Cekić [PDF]

Marked length spectrum

Marked length spectrum rigidity for Anosov surfaces, with Colin Guillarmou and Gabriel P. Paternain, Duke Math. J. 174, No. 1, 131-157 (2025) [PDF]
Local rigidity of manifolds with hyperbolic cusps II. Nonlinear theory, with Yannick Guedes Bonthonneau, J. Éc. Polytech., Math. 10, 1441-1510 (2023) [PDF]
Local rigidity of manifolds with hyperbolic cusps I. Linear theory and pseudodifferential calculus, with Yannick Guedes Bonthonneau, Ann. Inst. Fourier 73, No. 1, 335-421 (2023) [PDF]
Geodesic stretch, pressure metric and marked length spectrum rigidity, with Colin Guillarmou and Gerhard Knieper, Ergodic Theory Dynam. Systems 42 (2022), no. 3, 974–1022, special volume in memory of Anatole Katok [PDF]
The marked length spectrum of Anosov manifolds, with Colin Guillarmou, Ann. of Math. (2) 190 (2019), no. 1, 321–344 [PDF]. A talk by Ursula Hamenstädt at the Bourbaki seminar about our work.

Hyperbolic and partially hyperbolic dynamics

On the ergodicity of unitary frame flows on Kähler manifolds, with Mihajlo Cekić, Andrei Moroianu and Uwe Semmelmann, Ergodic Theory Dyn. Syst. 44, No. 8, 2143-2172 (2024) [PDF]
Isospectral connections, ergodicity of frame flows, and polynomial maps between spheres, with Mihajlo Cekić, Ann. Sci. Éc. Norm. Supér. (4) 58, No. 1, 203-229 (2025) [PDF]
On the ergodicity of the frame flow on even-dimensional manifolds, with Mihajlo Cekić, Andrei Moroianu and Uwe Semmelmann, Invent. Math. 238, No. 3, 1067-1110 (2024) [PDF]
Isometric extensions of Anosov flows via microlocal analysis, Commun. Math. Phys. 399, No. 1, 453-479 (2023) [PDF]
The Holonomy Inverse Problem, with Mihajlo Cekić, J. Eur. Math. Soc. (JEMS) 27, No. 6, 2187-2250 (2025) [PDF]
Towards Brin’s conjecture on frame flow ergodicity: new progress and perspectives, with Mihajlo Cekić, Andrei Moroianu and Uwe Semmelmann, Math. Res. Rep. 3 (2022), 21–34 [PDF]
Radial source estimates in Hölder-Zygmund spaces for hyperbolic dynamics, with Yannick Guedes Bonthonneau, Ann. Henri Lebesgue 6, 643-686 (2023). [PDF]
Classical and microlocal analysis of the X-ray transform on Anosov manifolds, with Sébastien Gouëzel, Anal. PDE 14 (2021), no. 1, 301–322 [PDF]

Generic dynamical systems

Generic injectivity of the X-ray transform, with Mihajlo Cekić, J. Differ. Geom. 129, No. 2, 261-334 (2025) [PDF]
Generic dynamical properties of connections on vector bundles, with Mihajlo Cekić, Int. Math. Res. Not. 2022, no. 14, 10649–10703 [PDF]
On the genericity of the shadowing property for conservative homeomorphisms, with Pierre-Antoine Guihéneuf, Proc. Amer. Math. Soc. 146 (2018), no. 10, 4225–4237 [PDF]

Inverse problems, tensor tomography, lens & boundary rigidity

Marked boundary rigidity for surfaces of Anosov type, with Alena Erchenko, Math. Z. 306, No. 3, Paper No. 36, 22 p. (2024). [PDF]
Stability estimates for the Holonomy Inverse Problem, with Mihajlo Cekić, Commun. Partial Differ. Equations 49, No. 5-6, 428-469 (2024). [PDF]
Invariant distributions and the transport twistor space of closed surfaces, with Jan Bohr and Gabriel P. Paternain, J. Lond. Math. Soc., II. Ser. 109, No. 5, Article ID e12894, 39 p. (2024) [PDF]
Local lens rigidity on manifolds of Anosov type, with Mihajlo Cekić, Colin Guillarmou, Anal. PDE 17, No. 8, 2737-2795 (2024) [PDF]
Boundary rigidity of negatively-curved asymptotically hyperbolic surfaces, Comment. Math. Helv. 95 (2020), no. 1, 129–166 [PDF]
Local marked boundary rigidity under hyperbolic trapping assumptions, J. Geom. Anal. 30 (2020), no. 1, 448–465 [PDF]
On the s-injectivity of the X-ray transform for manifolds with hyperbolic trapped set, Nonlinearity 32 (2019), no. 4, 1275–1295 [PDF]

Lévy flights

Geodesic Lévy flights and expected stopping time for random searches, with Yann Chaubet, Yannick Guedes Bonthonneau and Leo Tzou, Probab. Theory Relat. Fields 191, No. 1-2, 235-285 (2025) [PDF]

Riemannian geometry

Correspondence between Pestov and Weitzenböck identities, with Mihajlo Cekić, Andrei Moroianu and Uwe Semmelmann, Math. Proc. Camb. Philos. Soc. 178, No. 3, 443-463 (2025) [PDF]

Coauthors: Karen Butt, Jan Bohr, Mihajlo Cekić, Laurent Charles, Yann Chaubet, Alena Erchenko, Sébastien Gouëzel, Yannick Guedes Bonthonneau, Pierre-Antoine Guihéneuf, Colin Guillarmou, Tristan Humbert, Gerhard Knieper, Andrei Moroianu, Gabriel P. Paternain, Uwe Semmelmann, Leo Tzou, Amie Wilkinson.

Microlocal analysis in hyperbolic dynamics and geometry, Habilitation à diriger des recherches [PDF]
On the rigidity of Riemannian manifolds, Ph.D thesis under the supervision of Colin Guillarmou [PDF]
Introduction to inverse geometric problems, second master degree’s thesis, under the supervision of Colin Guillarmou [PDF]
Topological dynamics, first master degree’s thesis under the supervision of Alexander Arbieto, Research award of the Ecole Polytechnique [PDF]

Generic dynamical properties of connections on vector bundles, slides of a talk given online,
Geodesic stretch, pressure metric, marked length spectrum, video of a talk given at the online Pangolin Seminar,
On the rigidity of Riemannian manifolds, slides of my Ph.D defense, Orsay, France, December 2019,
Local rigidity of manifolds with hyperbolic cusps, slides of a talk given at the MSRI, Berkeley, USA, November 2019,
The X-ray transform on Anosov manifolds, video of a talk given at the conference « Probing the Earth with microlocal analysis », BIRS, Banff, Canada, April 2019. The slides are available here.

THIBAULT LEFEUVRE