Adrien Cances

Currently a PhD Student in my fourth (and last) year at the Laboratoire de Mathématiques d'Orsay, the primary focus of my research endeavours lies in optimal transport problems and some of their variations, particularly in the semi-discrete and multimarginal settings. 

I am a member of the INRIA-Saclay team ParMA (PARticle methods using Monge-Ampère), as well as of the ANR projects GOTA (Generalized Optimal Transport and Applications), SOCOT (Stochastic Orders and Constrained Optimal Transport), and of the PEPR project PDE-AI.

Research interest

The main focus of the thesis is the development of a particle discretization method to solve a nonlinear multi-marginal transport problem, motivated by risk estimation issues. This Lagrangian approach gives rise to various problems that are of particular interest to me: regularization of transport problems, uniform quantization of measures, as well as its numerical solution, semi-discrete partial transport, etc.

Seminars I am particularly interested in

Among others, I particularly enjoy the following seminars.

  • CalVa (Calculus of Variations)
  • OT-PDE-ML (Optimal Transport, Partial Differential Equations, Machine Learning)
  • CTOP (Convexity, Optimal Transport, Probabilités)

Contact

Room 2A1

Laboratoire de mathématiques d'Orsay
Build. 307
Université Paris-Saclay
91405 Orsay 

 

 Email

Firstname.LastnameATuniversite-paris-saclay.fr

Curriculum vitae

Short CV

 Publications/preprints

  • Unidimensional semi-discrete partial optimal transport
    Adrien Cances, Hugo Leclerc
    Submitted, preprint available
  • Particle method for a nonlinear multimarginal optimal transport problem
    Adrien Cances, Quentin Mérigot, Luca Nenna
    In preparation
  • An ODE characterization of a generalized semi-discrete optimal transport problem
    Adrien Cances, Luca Nenna, Daniyar Omarov, Brendan Pass
    In preparation
  • More to come in the next few months, stay tuned!

Selected talks

  • Risk estimation and partial optimal transport, Launch conference of the ANR project PDE-AI, Sorbonne Université, January 2024
  • Risk estimation via multimarginal optimal transport, Launch conference of the ANR project SOCOT (Stochastic Orders and Constrained Optimal Transport), Munster, February 2024
  • Optimal quantization of measures, Zador's theorem, and a recent generalization to uniform quantization, CTOP seminar (Convexity, Optimal Transport, Probabilities), Henri Poincaré Institute, October 2024
  • Particle methods for high-dimensional multi-marginal optimal transport, PGMO Days, EDF Lab Paris-Saclay, November 2024
  • Semi-discrete partial optimal transport, the case of dimension 1, PhD student's seminar of the Laboratoire Jacques-Louis Lions, Sorbonne Université, April 2025
  • Particle methods for a nonlinear multi-marginal optimal transport, PGMO Days, EDF Lab Paris-Saclay, November 2025
  • Uniform quantization of measures, PhD student's seminar of the Laboratoire de Mathématiques d'Orsay, December 2025

To come

  • C-cyclical monotonicity : a generalization of Rockafellar's and Brenier's respective theorems, PhD student's seminar of the Laboratoire de Mathématiques d'Orsay, room 2L8, on January 7 2025, at 14:00

Teaching

  • 2022-2023: IUT de Sceaux, second-year students , Probabilities in the 1st semester, Statistics in the 2nd semester
  • 2023-2024: Faculté des Sciences d'Orsay, second-year students, Numerical analysis for ODEs, in the 1st semester,
  • 2024-2025: Faculté des Sciences d'Orsay, second-year students, Analysis in the 1st semester, Topology in the 2nd semester

Other

Contribution to the laboratory life

  • 2023-2025 : co-organization, together with Salammbo Connolly, of the biweekly PhD student's seminar of the laboratory (meant not only for the PhD students of all five teams of Orsay, but also for any PhD student in mathematics willing to attend)
    • Please feel free to contact the current organizers Louis-Ibrahim Louis-Brahim Beaufort and Yannis Monbru-Carcelero, if you would like to attend and/or be added to the mailing list!
  • 2023-2024 : one of the eight PhD student representatives at the Hadamard Doctoral School of Mathematics (EDMH)

Posters

  • Partial optimal transport and risk estimation, SMAI MODE Days, INSA Lyon, March 2024
  • Partial optimal transport and risk estimation, PEPR IA Days, CentraleSupélec, March 2025
  • Multimarginal transport and risk estimation, First national meeting of the RT Optimisation, INSA Lyon, November 2025