Introduction

Research Topic

This PhD focuses on the study of efficient algorithms for multimarginal and martingale constraints optimal transportation problems.

Optimal tranportation problems have various applications both in finance, in economy or in physics. In particular, we want to apply our algorithm to the computation of the Lévy-Lieb functional used in the Density Functional Theory.

However, in the case of multimarginal constraints optimal transportation problem, current algorithms scale exponentially in the number of marginal laws; which forbids the computation of the transport for large systems. We aim to have an algorithm with a linear scale using a particle algorithm.

Publications & Preprints

• A. Alfonsi, R. Coyaud and V. Ehrlacher Constrained overdamped Langevin dynamics for symmetric multimarginal optimal transportation
• É. Cancès, R. Coyaud and L. R. Scott Van der Waals interactions between two hydrogen atoms: The next orders
• A. Alfonsi, R. Coyaud, V. Ehrlacher and D. Lombardi Approximation of optimal transport problems with marginal moments constraints (preprint)

Conferences and Talks

• MOANSI annual meeting 2020, online, 25/09-25/09/2020 (slides, video)
• Advances in Financial Mathematics 2020, Paris, France, 14/01-17/01/2020 (slides)
• People in Optimal Transportation and Applications, Cortona, Italy, 24/06-28/06/2019 (slides)
• Optimal Transport: from Geometry to Numerics, Vienna, Austria, 13/05-17/05/2019
• Optimal Transport Methods in Density Functional Theory, Banff, Canada, 27/01-01/02/2019 (slides)
• Mass Transportation Theory: Opening perspectives in Statistics, Probability and Computer Science, Valladolid, Spain, 04/06-08/06/2018
• Summer School, Optimal transport: numerical methods and applications, Lake Como School of Advanced Studies, Como, Italy, 07/05-11/07/2018
• Mini-school on mathematics in electronic structure theory GdR Corrélation Électronique, Paris, France, 09/01-11/01/2017

Teaching

• Optimization, 1A École des Ponts ParisTech
• Analyse et Calcul Scientifique, 1A École des Ponts ParisTech

Curriculum

I am a former student of École Polytechnique and Pierre and Marie Curie University. A detailed resume can be found here (English version) and here (French version).

Contact