Publications and preprints

2022–2024

• Nonnegative cross-curvature in infinite dimensions: synthetic definition and spaces of measures
  Flavien Léger, Gabriele Todeschi, François-Xavier Vialard.
  arXiv:2409.18112, 2024.
• A geometric approach to apriori estimates for optimal transport maps
  Simon Brendle, Flavien Léger, Robert J. McCann and Cale Rankin.
  J. Reine Angew. Math. (2024), no. 0
• 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 and Applied Analysis 5 (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.
  Advances in Neural Information Processing Systems (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.
  In Proc. NeurIPS’20, 2020.
• A gradient descent perspective on Sinkhorn
  Flavien Léger.
  Appl. Math. Opt., 2020.
• 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.
  Journal of Differential Equations, 2020.
• 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.

2011–2018

• A geometric perspective on regularized optimal transport
  Flavien Léger.
  J. Dyn. Diff. Equat., 2018.
• 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.