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