Publications and preprints

2022–2025

• A comparison principle for variational problems, with applications to optimal transport
  Flavien Léger and Maxime Sylvestre.
  arXiv:2506.18884, 2025.
• Nonnegative cross-curvature in infinite dimensions: synthetic definition and spaces of measures
  Flavien Léger, Gabriele Todeschi, François-Xavier Vialard.
  Accepted in Geom. Funct. Anal. (2025)
• A geometric approach to apriori estimates for optimal transport maps
  Simon Brendle, Flavien Léger, Robert J. McCann and Cale Rankin.
  J. Reine Angew. Math. 817 (2024), 251–266.
• Gradient descent with a general cost
  Flavien Léger and Pierre-Cyril Aubin-Frankowski.
  arXiv:2305.04917, 2023.
  [Slides]
• A geometric Laplace method
  Flavien Léger and François-Xavier Vialard.
  Pure Appl. Anal. 5 (2023), no. 4, 1041–1080.
• Mirror Descent with Relative Smoothness in Measure Spaces, with application to Sinkhorn and EM
  Pierre-Cyril Aubin-Frankowski, Anna Korba and Flavien Léger.
  NeurIPS 2022.

2019–2021

• The back-and-forth method for Wasserstein gradient flows
  Matt Jacobs, Wonjun Lee and Flavien Léger.
  ESAIM Control Optim. Calc. Var. 27 (2021).
  [Project page] [Code] [Slides]
• Faster Wasserstein Distance Estimation with the Sinkhorn Divergence
  Lénaïc Chizat, Pierre Roussillon, Flavien Léger, François-Xavier Vialard and Gabriel Peyré.
  NeurIPS 2020.
• A gradient descent perspective on Sinkhorn
  Flavien Léger.
  Appl. Math. Optim. 84 (2021), no. 2, 1843–1855.
• A fast approach to optimal transport: The back-and-forth method
  Matt Jacobs and Flavien Léger.
  Numerische Mathematik (2020): 1-32.
  [Project page] [Code] [Slides]
• Hopf–Cole transformation via generalized Schrödinger bridge problem
  Flavien Léger and Wuchen Li.
  J. Differential Equations 274 (2021), 788–827.
• Solving large-scale optimization problems with a convergence rate independent of grid size
  Matt Jacobs Flavien Léger, Wuchen Li and Stanley Osher.
  SIAM J. Numer. Anal. 57 (2019), no. 3, 1100–1123.

2011–2018

• A geometric perspective on regularized optimal transport
  Flavien Léger.
  J. Dynam. Differential Equations 31 (2019), no. 4, 1777–1791.
• A new approach to bounds on mixing Flavien Léger.
  Math. Models Methods Appl. Sci., 28(5):829–849, 2018.
  [Slides]
• Aggregation via the Newtonian potential and aggregation patches
  Andrea Bertozzi, Thomas Laurent and Flavien Léger.
  M3AS, vol. 22, Supp. 1, 2012.
  [Project page]
• Efficient Matrix Completion with Gaussian Models
  Flavien Léger, Guoshen Yu and Guillermo Sapiro.
  In IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), 2011.