Vincent Divol

Ph.D. Thesis

Here is my Ph.D. thesis manuscript. You can find the corresponding slides there, and a video recording of the defense itself there.

Preprints

  1. Arnal C., Cohen-Steiner D., Divol, V. (2023). Critical points of the distance function to a generic submanifold. arxiv
  2. Divol, V., Niles-Weed J., Pooladian A-A. (2022). Optimal transport map estimation in general function spaces. arxiv
  3. Divol, V. (2021). A short proof on the rate of convergence of the empirical measure for the Wasserstein distance. arxiv

Published

  1. Pooladian A-A., Divol, V., Niles-Weed J., (2023). Minimax estimation of discontinuous optimal transport maps: The semi-discrete case. 40th International Conference on Machine Learning (ICML 2023). PMLR. proceedings (equal contributions)
  2. Divol, V. (2022). Measure estimation on manifolds: an optimal transport approach. Probability Theory and Related Fields. journal
  3. Divol, V. (2021). Minimax adaptive estimation in manifold inference. Electronic Journal of Statistics. journal
  4. Divol, V., & Lacombe, T. (2021). Estimation and Quantization of Expected Persistence Diagrams. 38th International Conference on Machine Learning (ICML 2021). PMLR. proceedings
  5. Divol, V., & Lacombe, T. (2021). Understanding the topology and the geometry of the space of persistence diagrams via optimal partial transport. Journal of Applied and Computational Topology. journal
  6. Divol, V., & Chazal, F. (2019). The density of expected persistence diagrams and its kernel based estimation. Journal of Computational Geometry. journal
  7. Divol, V., & Polonik, W. (2019). On the choice of weight functions for linear representations of persistence diagrams. Journal of Applied and Computational Topology. journal
  8. Chazal, F., & Divol, V. (2018). The density of expected persistence diagrams and its kernel based estimation. 34th International Symposium on Computational Geometry (SoCG 2018). proceedings