Research in differential geometry at IMAG, in the GTA team.

I belong to the French research groups RT2182 Tétraèdre (previously GDR Platon) and to the ANR project GAPR.

Corganizer of the weekly seminar Séminaire Darboux at Montpellier.

Teaching at the mathematics department of Faculté des Sciences de Montpellier.

News

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July 1-4 2024, workshop Geometry and Analysis on metric surfaces , Warsaw, Poland.

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April 15-19 2024, conference of the ANR project GAPR, Submanifolds of locally symmetric spaces: geometric, analytic and dynamical aspects Autrans, France.

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Earlier

2023

Publications

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Polyhedral surfaces in flat (2+1)-spacetimes and balanced cellulations on hyperbolic surfaces,
with Roman Prosanov
Preprint arxiv 

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An Introduction to Reshetnyak’s Theory of Subharmonic Distances,
in Reshetnyak's Theory of Subharmonic Metrics, CRM-Springer 2023 article arxiv 

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Hyperbolic geometry of shapes of convex bodies,
with Clément Debin.
Groups, Geometry, and Dynamics 2022. article

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A remark on one-harmonic maps from a Hadamard surface of pinched negative curvature to the hyperbolic plane,
with Andrea Seppi.
Josai Mathematical Monographs 2021 article

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Generalization of a formula of Wolpert for balanced geodesic graphs on closed hyperbolic surfaces,
with Andrea Seppi.
Annales Henri Lebesgue 2020 article

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Quasi-Fuchsian co-Minkowski manifolds,
with Thierry Barbot.
in In the tradition of Thurston, Springer Cham, 2020 article arxiv

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A note on invariant constant curvature immersions in Minkowski space,
with Graham Smith,
Geometriae Dedicata, 2020 article arxiv

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Embeddings of non-positively curved compact surfaces in flat Lorentzian manifolds,
with Dmitriy Slutskiy,
Mathematische Zeitschrift, 2019 article arxiv

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Spherical, hyperbolic and other projective geometries: convexity, duality, transitions,
with Andrea Seppi,
in Eighteen Essays in Non-Euclidean Geometry, 2019 article arxiv

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Group actions and scattering problems in Teichmüller theory,
with Graham Smith,
in Handbook of group action IV, 2018 article arxiv

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The equivariant Minkowski problem in Minkowski space,
with Francesco  Bonsante.
Ann. Inst. Fourier , 2017 article

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A remark on spaces of flat metrics with cone singularities of constant sign curvatures,
with Ivan Izmestiev.
Sémin. Théor. Spectr. Géom. 2017 article

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A short elementary proof of reversed Brunn–Minkowski inequality for coconvex bodies
Sémin. Théor. Spectr. Géom. 2017 article

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Shapes of polyhedra, mixed volumes, and hyperbolic geometry,
with Ivan Izmestiev.
Mathematika, 2017 article arxiv

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Lorentzian area measures and the Christoffel problem,
with Giona Veronelli.
Ann. Sc. Norm. Super. Pisa, 2016 article

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Hyperbolization of cusps with convex boundary,
with Ivan Izmestiev and Giona Veronelli.
Manuscripta Math., 2016 article arxiv

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Christoffel and Minkowski problems in Minkowski space,
Théor. Spectr. Géom. 2015 article

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Polygons of the Lorentzian plane and spherical simplexes,
Elem. Math., 2014 article

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Fuchsian convex bodies: basics of Brunn--Minkowski theory,
Geom. Funct. Anal. 2013 article

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Flippable tilings of constant curvature surfaces,
with Jean-Marc Schlenker.
Illinois J. Math., 2012 article

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Gauss images of hyperbolic cusps with convex polyhedral boundary, with Ivan Izmestiev.
Trans. Am. Math. Soc., 2011 article

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Fuchsian polyhedra in Lorentzian space-forms,
Mathematische Annalen, 2011 article arxiv

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From spaces of polygons to spaces of polyhedra following Bavard, Ghys and Thurston,
Enseign. Math., 2011 article

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Existence and uniqueness theorems for convex polyhedral metrics on compact surfaces,
in Current problems in mathematics and mechanics. Vol. VI, 2010 arxiv

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Hyperbolic cusps with convex polyhedral boundary,
with Ivan Izmestiev.
Geometry and Topology, 2009 article

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Polyhedral hyperbolic metrics on surfaces,
Geom. Dedicata, 2008 Erratum Geom. Dedicata 2009 article arxiv

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Polyhedral realisation of hyperbolic metrics with conical singularities on compact surfaces,
Ann. Inst. Fourier, 2007 article

Supervisor

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Hicham Labeni, PhD Cergy 2016-2020
Realizing metrics of curvature \leq −1 on closed surfaces in Fuchsian anti-de Sitter manifolds
Journal of the Australian Mathematical Society, 2021 article arxiv

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Dmitriy Slutskiy, Post doc Cergy 2015-2016
Embeddings of non-positively curved compact surfaces in flat Lorentzian manifolds
Mathematische Zeitschrift, 2019 article arxiv

Vitae

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I graduated in 2006 under the supervisation of Bruno Colbois (Neuchâtel) and Jean-Marc Schlenker (Toulouse ---now Luxembourg). I spent one year post doc position in Friboug (CH) under the supervision of Ruth Kellerhals I was a Maître de Conférence at Université de Cergy-Pontoise (now called CYU), then I moved to Université de Montpellier in 2020 on the basis of an greement, and then formally in 2022.

I spent the academic year 2019-2020 at the IRL CRM-CNRS at Université de Montréal

During the Covid lockdown, we ran the online Pangolin Seminar (2020-2021) with some colleagues.