Quantitative Uniqueness of Kantorovich Potentials
Uniqueness criteria and quantitative bounds for Kantorovich potentials, including measures supported on lower-dimensional sets.
William Ford
PhD student in mathematics — École Polytechnique (CMAP) & LMO Paris-Saclay
About
I am a PhD student in mathematics in Paris, advised by Michael Goldman and Cyril Letrouit. I am based at the Centre de Mathématiques Appliquées at École Polytechnique and the Laboratoire de Mathématiques d'Orsay. I am also a member of the Inria ParMA team and the shape optimisation team at CMAP, École Polytechnique.
My research is in optimal transport. I am currently working on the uniqueness and quantitative stability questions for both the primal and dual optimal transport problems. I recently released a first paper on this subject, regarding uniqueness of solutions to the dual problem, see below.
Contact: william.ford@polytechnique.edu. Offices: 2A1 at LMO and 2008 at CMAP.
You can find my CV HERE.
Preprints
Quantitative Stability in Discrete Optimal Transport
Stability of discrete optimal transport under perturbations, with extensions of convexity and dual uniqueness results.
Talks
Quantitative Uniqueness of Kantorovich Potentials
Poster presentations
Visits
- : Upcoming research visit to Filippo Santambrogio in Lyon, France.
Education
- 2025–2028: PhD in Mathematics, École Polytechnique & LMO Paris-Saclay.
- 2024–2025: M2 Mathematics, Optimisation track, Institut Polytechnique de Paris / Paris-Saclay.
- 2020–2024: BSc and MSc Mathematics, Durham University.
Theses
- M2 thesis: Quantitative Stability in Discrete Optimal Transport .
- MSc thesis: Partial Regularity for Optimal Transport Maps between Uniform Measures .
- BSc thesis: Normal Families in Complex Analysis .
Responsibilities
- Co-organiser of the GdT OT-PDE-ML seminar (ParMA team, LMO Paris-Saclay).