CV   |   Research interests   |   Publications and Preprints   |   Other documents   |   Talks   |   Teaching   |   Supervision  

Martin Mion-Mouton Pour voir cette page en français, aller ici. Address Max Planck Institute for Mathematics in the Sciences Inselstraße 22 04103 Leipzig Germany Office: G2 07 E-mail: martin.mion [at] mis.mpg.de Link to my ORCID record: https://orcid.org/0000-0002-8814-0918. Link to my papers on arXiv: https://arxiv.org/a/mionmouton_m_1.html. Link to my papers on HAL: https://cv.archives-ouvertes.fr/martin-mion-mouton.

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Welcome on my personal webpage !

I am currently a post-doc in Mathematics at the Max-Planck institute for Mathematics in the sciences in Leipzig, working in Anna Wienhard's Geometry, Groups, and Dynamics research group.

I defended my PhD in December 2020 at Strasbourg's University under the supervision of Charles Frances. Until September 2021 I was ATER (temporary teacher and researcher) at Strasbourg's University, and in 2021-2023 I was a postdoctoral fellow at the Mathematics department of the Technion in Haifa, working with Tali Pinsky.

Here is my CV for more informations (updated in march 2024).

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Research Interests

I am interested in differentiable dynamical systems in connection with geometric structures, and in the informations (and possible rigidity) that such interactions may give - on the dynamics or on the geometry.

My work is related to the folllowing subjects (whose list is highly non-exhaustive):

• Rigid geometric structures, Parabolic Cartan geometries, Path geometries, Flag structures in dimension 3;
• Partially Hyperbolic diffeomorphisms, Anosov flows;
• Singular Lorentzian surfaces; Interval exchange maps.

Here is a short research project written in english in december 2023, describing my past work, and current and future research projects. Here is a longer research project written in french in march 2024.

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Publications and Preprints

Publications

1. Geometrical compactifications of geodesic flows and path structures. Geometriae Dedicata 217(2) (2022), 18. (arXiv:2112.02900, hal-03466455)
2. Cartan connections and path structures with large automorphism groups (with Elisha Falbel and Jose Miguel Veloso). International Journal of Mathematics 32(12) (2021). (arXiv:2105.02090, hal-03214060)
3. Partially hyperbolic diffeomorphisms and Lagrangian contact structures. Ergodic Theory and Dynamical Systems 42(8) (2022), 2583-2629. (arXiv:2002.10720, hal-02489310)

The preprint versions may differ with the published one.

In preparation

1. Rigidity of singular de-Sitter tori with respect to their lightlike foliations.
2. Surgeries of three-dimensional flag structures and non-uniformizable examples (with E. Falbel).

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Other documents

• This short text is a summary of some folklore results about distributions invariant by Anosov flows and Partially hyperbolic diffeomorphisms, which are quite known but whose proofs are less, and spread out in the literature. I prove a result for which I could not find references, and outline the way to find the proofs of the other results in the literature.
• This short text contains details about a result used in the paper 1 of the above list, which links coverings to the property of path-lifting in the directions of a splitting within one-dimensional distributions.
• The manuscript of my Ph.D thesis entitled Some geometrical and dynamical properties of Lagrangian contact structures (essentially in french, with one chapter and an abstract in english).
• In september 2017, I defended my Master thesis at the university of Strasbourg under the supervision of Charles Frances, entitled Contact Anosov flows in dimension three, through associated Lagrangian contact structures (the manuscript is in french).

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Talks

• Geometry and Topology seminar, university of Luxembourg, April 2024.
• Spectral theory and Geometry seminar, Grenoble university, March 2024.
• Conference Aspects of ergodic theory for hyperbolic groups, Leipzig university, March 2024 (contributed talk).
• seminar of Ergodic theory and dynamical systems, university Paris-13, February 2024.
• Ergodic theory seminar, Rennes university, February 2024.
• Geometry and Topology seminar, Aix-Marseille university, February 2024.
• Geometry seminar, Max-Planck institute for Mathematics in the Sciences, Leipzig, October 2023.
• Conference Anosov systems, CIRM, Luminy, April 2023 (short talk).
• Geometry and Topology seminar, Sorbonne university, February 2023.
• Differential Geometry seminar, Heidelberg university, January 2023.
• Conference Complex Hyperbolic Geometry and Related Topics, CIRM, June 2022.
• Conference Geometric structures, compactications and group actions, Strasbourg university, June 2022 (short talk).
• Geometry and Topology seminar, Technion, March 2022.
• Seminar The mathematics of motion, Technion, March 2022.
• Geometry seminar, Bordeaux university, October 2021.
• Darboux seminar, Montpellier university, October 2021.
• Seminar of dynamical systems and Geometry, Angers university, March 2021.
• Teich Seminar, Aix-Marseille university, March 2021.
• Geometry, Topology and Dynamic seminar, Paris-Saclay university (Orsay), February 2021.
• Ergodic theory and Dynamical systems seminar, Paris 13 university (LAGA), February 2021.
• Jeunes géomètres dynamiques, GDR Platon conference, December 2020.
• Conference First Joint Meeting Brazil-France in Mathematics (session 10), IMPA (Rio de Janeiro, Brésil), August 2019.

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Teaching

I will not teach this year, but you can find in my CV a full description of my many past teaching, supervising and outreach activities.

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Supervision

In 2021, I supervised the master's thesis of Justin Rieber (M2 agrégation), whose subject was Poincaré-Bendixson Theorem. Justin is now a high-school teacher.