Quentin Mérigot’s homepage

Teaching

I am the coordinator of M2 Optimization, a master program involving Université Paris-Sud, École Polytechnique, ENSTA, Centrale-Supélec and HEC. In addition, I also teach the following courses:

• M315: Algorithmes d’optimisation (L3),
• M1MAO: Calcul scientifique (M1),
• M2OT: Optimal transport (M2)

Research

My research interests include optimal transport and its applications, inverse problems, discretization of PDEs and geometric methods for data analysis. The numerical methods I propose often rely on techniques from optimization and computational geometry. I coordinate the Monge-Ampère et Géométrie Algorithmique project, funded by the French national research agency (ANR).

• A damped Newton algorithm for generated Jacobian equations
  Anatole Gallouët, Quentin Merigot, Boris Thibert
  
• Optimal transport: discretization and algorithms
  Quentin Mérigot, Boris Thibert,
  In Handbook of Numerical Analysis 22 – Geometric PDES
• 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), to appear
• 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.

Contact

E-mail: Firstname.Lastname@math.u-psud.fr
Phone: +33 (0)1 69 15 57 59

Address: Laboratoire de Mathématiques d’Orsay
Bâtiment 307 (Institut de Mathématique, bureau 2D1
Faculté des Sciences d’Orsay Université Paris-Sud
91405 Orsay Cedex