Quentin Mérigot’s homepage

Professor in applied mathematics at Université Paris-Saclay.
Junior member of the Institut universitaire de France (IUF).

E-mail: Firstname.Lastname@universite-paris-saclay.fr
Phone: +33 (0)1 69 15 57 59
Address: Institut de Mathématique d'Orsay (Building 307, Office 2D1)
Faculté des Sciences d'Orsay, 91405 Orsay Cedex

Teaching

I am the director of Master in Optimization, a master program of Université Paris-Saclay and Institut Polytechnique de Paris. I teach or taught the following courses: Convex analysis and optimization (M2), Optimization (L3), Numerical analysis (M1), Optimal transport (M2) and at IHP.

Research

My research interests include optimal transport, inverse problems, numerical analysis and geometric methods for data analysis. The numerical methods I propose often rely on techniques from optimization and computational geometry.

Current projects: PEPR PDE-AI, OT @ Lagrange

Preprints

• Strong c-concavity and stability in optimal transport
  Anatole Gallouët, Quentin Mérigot, Boris Thibert
• Gluing methods for quantitative stability of optimal transport maps
  Cyril Letrouit, Quentin Mérigot

Articles

• Quantitative Stability of the Pushforward Operation by an Optimal Transport Map
  Guillaume Carlier, Alex Delalande, Quentin Mérigot
  Foundations of Computations Mathematics, 2024 [doi]
• Robust risk management via multi-marginal optimal transport
  Hamza Ennaji, Quentin Mérigot, Luca Nenna, Brendan Pass
  Journal of Optimization Theory and Applications, 202, 2024 [doi]
• Quantitative Stability of Optimal Transport Maps under Variations of the Target Measure
  Alex Delalande, Quentin Mérigot
  Duke Mathematical Journal, 172(17), 2023 [doi]
• Quantitative Stability of Barycenters in the Wasserstein Space
  Guillaume Carlier, Alex Delalande, Quentin Merigot
  Probability Theory and Related Fields, 2023 [doi]
• Metasurfaces and Optimal transport
  Cristian E. Gutiérrez, Qingbo Huang, Quentin Mérigot, Boris Thibert
  Journal of Computational Mathematics 22(8), 2022
• Convergence of a Lagrangian discretization for barotropic fluids and porous media flow
  Thomas Gallouët, Quentin Mérigot, Andrea Natale
  SIAM J. Mathematical Analysis 54(3), 2022 [doi]
• Non-asymptotic convergence bounds for Wasserstein approximation using point clouds
  Quentin Mérigot, Filippo Santambrogio, Clément Sarrazin,
  Proceedings of Advances in Neural Information Processing Systems 34 (NeurIPS 2021)
• A damped Newton algorithm for generated Jacobian equations
  Anatole Gallouët, Quentin Merigot, Boris Thibert
  Calculus of variations and partial differential equations 61(49), 2022
• Optimal transport: discretization and algorithms
  Quentin Mérigot, Boris Thibert,
  In Handbook of Numerical Analysis 22 – Geometric PDES, p133-212 [doi]
• Quantitative stability of optimal transport maps and linearization of the 2-Wasserstein space
  Quentin Mérigot, Alex Delalande, Frédéric Chazal,
  Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics (AISTATS 2020), PMLR 108:3186-3196, 2020.
• Lagrangian discretization of crowd motion and linear diffusion
  Hugo Leclerc, Quentin Mérigot, Federico Stra, Filippo Santambrogio,
  SIAM J. Numerical Analysis, 58(4), 2093–2118, 2020.
• One more proof of the Alexandrov-Fenchel inequality
  Dario Cordero-Erausquin, Bo’az Klartag, Quentin Mérigot, Filippo Santambrogio,
  Compte-rendus de l’académie des sciences, 357 (8), 2019.
• Light in Power: A General and Parameter-free Algorithm for Caustic Design
  Quentin Mérigot, Jocelyn Meyron, Boris Thibert
  ACM Transaction on Graphics (TOG, Proc SIGGRAPH Asia), 37(6), 2018.
• An algorithm for optimal transport between a simplex soup and a point cloud
  Quentin Mérigot, Jocelyn Meyron, Boris Thibert
  SIAM Journal on Imagins Science (SIIMS), 11(2), 1363–1389, 2018 [doi]
• A Lagrangian scheme à la Brenier for the incompressible Euler equations
  Thomas Gallouët, Quentin Mérigot
  Foundation of Computational Mathematics (FOCM), 18(4), 835–865, 2018 [doi]
• Convergence of a Newton algorithm for semi-discrete optimal transport
  Jun Kitagawa, Quentin Mérigot, Boris Thibert
  Journal of the European Math Society (JEMS), 21(19), 2019, 2603–2651
• Inference of curvature using tubular neighborhoods,
  Frédéric Chazal, David Cohen-Steiner, André Lieutier, Quentin Mérigot, Boris Thibert
  In Modern approaches to discrete curvature 133–158, Springer LNM, 2017
• Minimal geodesics along volume preserving maps, through semi-discrete optimal transport
  Quentin Mérigot, Jean-Marie Mirebeau
  SIAM J. Numerical Analysis (SINUM), 54(6), 3465–3492, 2016 [doi]
• Discretization of functionals involving the Monge-Ampère operator
  Jean-David Benamou, Guillaume Carlier, Quentin Mérigot, Édouard Oudet
  Numerische Mathematik 134 (3), 611-636, 2016 [doi]
• Far-field reflector problem and intersection of paraboloids
  Pedro Machado Manhães de Castro, Quentin Mérigot, Boris Thibert
  Numerische Mathematik 134 (2), 389-411, 2016 [doi] (also Proc. SoCG 2014 [doi])
• An optimal transport approach for seismic tomography: application to 3D FWI
  Ludovic Métivier, Romain Brossier, Quentin Mérigot, Édouard Oudet, Jean Virieux
  Inverse Problems, 32 (11), 2016 [doi]
• Measuring the misfit between seismograms using an optimal transport distance: application to full waveform inversion
  Ludovic Métivier, Romain Brossier, Quentin Mérigot, Édouard Oudet, Jean Virieux
  Geophysical Journal International (GJI), 205 (1), 345-377, 2016 [doi]
• Handling convexity-like constraints in variational problems
  Quentin Mérigot, Édouard Oudet
  SIAM Journal on Numerical Analysis (SINUM), 52 (5), 2466–2487, 2014 [doi].
• Robust Geometry Estimation using the Generalized Voronoi Covariance Measure
  Louis Cuel, Jacques-Olivier Lachaud, Quentin Mérigot, Boris Thibert
  SIAM Journal on Imaging Science (SIIMS), 8(2), 1293–1314, 2015 [doi].
• On the reconstruction of convex sets from random normals measurements
  Hiba Abdallah, Quentin Mérigot
  Discrete and Computational Geometry (DCG) 53(3), 569–586, 2015 (also Proc SoCG 2014) [doi]
• Discrete optimal transport: complexity, geometry and applications
  Quentin Mérigot, Édouard Oudet
  Discrete and Computational Geometry (DCG), 55(2), 263–283, 2016 [doi]
• Far-field reflector problem under design constraints
  Julien André, Dominique Attali, Quentin Mérigot, Boris Thibert
  Int. J. of Computational Geometry and Applications (IJCGA), 25 (2), 143-162, 2015 [doi].
• A comparison of two dual methods for discrete optimal transport.
  Quentin Mérigot
  Geometric Science of Information, Springer LNCS 8085, 389-396, 2013 [doi]
• Lower bounds for k-distance approximation.
  Quentin Mérigot
  Proceedings of the 29th ACM Symposium on Computational Geometry, 2013 [doi]
• Shape Matching via Quotient Spaces.
  Maks Ovsjanikov, Quentin Mérigot, Viorica Pătrăucean, Leonidas Guibas
  Computer Graphics Forum 32 (5) 1–11, 2013 (also Proc SGP 2013) [doi].
• Witnessed k-distance.
  Leonidas Guibas, Quentin Mérigot, D. Morozov
  Discrete and Computational Geometry (DCG), 49 (1) 22–45, 2013 (also Proc SoCG 2011) [doi].
• A multiscale approach to optimal transport.
  Quentin Mérigot
  Computer Graphics Forum 30 (5) 1583–1592, 2011 (also Proc SGP 2011) [doi].
• Size of the medial axis and stability of Federer’s curvature measures
  Quentin Mérigot
  In Optimal Transportation: Theory and Applications, London Mathematical Society Lecture Note Series 413, pp 288–306 [doi]
• Geometric inference for probability measures.
  Frédéric Chazal, David Cohen-Steiner, Quentin Mérigot
  Foundation of Computational Mathematics (FOCM) 11, 733-751 (2011) [doi].
• Boundary measures for geometric inference.
  Frédéric Chazal, David Cohen-Steiner, Quentin Mérigot
  Foundation of Computational Mathematics (FOCM)10, 221-240 (2010) [doi].
• Feature Preserving Mesh Generation from 3D Point Clouds.
  Nader Salman, Mariette Yvinec, Quentin Mérigot
  Computer Graphics Forum 29 (5) 1623–1632, 2010 (also Proc. SGP 2010) [doi].
• One Point Isometric Matching with the Heat Kernel.
  Maks Ovsjanikov, Quentin Mérigot, Facundo Mémoli, Leonidas Guibas
  Computer Graphics Forum 29 (5) 1555–1564, 2010 (also Proc. SGP 2010) [doi].
• Voronoi-based Curvature and Feature Estimation from Point Clouds.
  Quentin Mérigot, Maks Ovsjanikov, Leonidas Guibas
  IEEE Transactions on Visualization and Computer Graphics (TVCG) 17 (6) 743–756, 2011 [doi].
• Anosov AdS representations are quasi-Fuchsian.
  Thierry Barbot, Quentin Mérigot
  Groups, Geometry and Dynamics 6(3), 441-483 (2012) [doi].

Theses

• From geometric inference to computational optimal transport
  Habilitation à diriger les recherches, Université de Grenoble, 2014.
• Geometric structure detection in point clouds
  Thèse de doctorat, Université de Nice Sophia-Antipolis, 2009.

Students and postdocs

PhD Students: Alex Delalande (2019–, with Frédéric Chazal), Anatole Gallouët (2019–, with Boris Thibert) Clément Sarrazin (2018–, with Filippo Santambrogio), Jocelyn Meyron (2015-2018, with Boris Thibert), Julien André (2012-2015, with Boris Thibert and Dominique Attali)

Post-docs: Jean-Baptiste Keck (2020-21, with Boris Thibert) Andrea Natale (2020-21, with Thomas Gallouët), Federico Stra (2018-19, with Filippo Santambrogio) Thomas Gallouët (2016-17, with Yann Brenier) Hiba Abdallah(2011-12)