Publications

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Preprints

 

• The Holonomy Inverse Problem, with Mihajlo Cekić,
• Geometric inverse problems on Anosov manifolds, preliminary version, still under construction (comments are welcome!), 
• Radial source estimates in Hölder-Zygmund spaces for hyperbolic dynamics,  with Yannick Guedes Bonthonneau,
• Local rigidity of manifolds with hyperbolic cusps II. Nonlinear theory, with Yannick Guedes Bonthonneau

Geometric inverse problems

• Local rigidity of manifolds with hyperbolic cusps I. Linear theory and pseudodifferential calculus, with Yannick Guedes Bonthonneau, to appear in Annales de l’Institut Fourier.
• The marked length spectrum of Anosov manifolds, with Colin Guillarmou, Ann. of Math. (2) 190 (2019), no. 1, 321–344.
• Boundary rigidity of negatively-curved asymptotically hyperbolic surfaces, Comment. Math. Helv. 95 (2020), no. 1, 129–166.
• Local marked boundary rigidity under hyperbolic trapping assumptions, J. Geom. Anal. 30 (2020), no. 1, 448–465.
• On the s-injectivity of the X-ray transform for manifolds with hyperbolic trapped set, Nonlinearity 32 (2019), no. 4, 1275–1295.

Dynamical systems

• Generic dynamical properties of connections on vector bundles, with Mihajlo Cekić, to appear in International Mathematics Research Notices.
• Geodesic stretch, pressure metric and marked length spectrum rigidity, with Colin Guillarmou and Gerhard Knieper, to appear in Ergodic Theory and Dynamical Systems, special volume in memory of Anatole Katok.
• Classical and microlocal analysis of the X-ray transform on Anosov manifolds, with Sébastien Gouëzel, to appear in Analysis and PDE (2019)
• On the genericity of the shadowing property for conservative homeomorphisms, with Pierre-Antoine Guihéneuf, Proc. Amer. Math. Soc. 146 (2018), no. 10, 4225–4237.

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Slides

• 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. 

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Unpublished texts

• On the rigidity of Riemannian manifolds, the manuscript of my thesis,
• Introduction to inverse geometric problems, second master degree’s thesis, under the supervision of Colin Guillarmou,
• Topological dynamics, first master degree’s thesis, under the supervision of Alexander Arbieto, Research award of the Ecole Polytechnique,
• A poster explaining my research (in french), presented at the conference « Echos des Sciences », Orsay, March 2018,
• From the local to the global injectivity of the X-ray transform, a note presented at the conference « Analytic studies of flows », Peyresq, June 2018

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