Computational Optimal Transport

In the last 30 years, the theory of optimal transportation (OT) has emerged as a fertile field of inquiry, and a diverse tool for exploring applications within and beyond mathematics, in such diverse fields as economics, meteorology, geometry, fluid mechanics and engineering. More recently, thanks to many applications in finance, economics, quantum chemistry, machine learning and statistics, the OT theory for finitely many marginals has achieved important results and is growing considerably.

Despite the enormous amount of progress in the mathematical and scientific literature, computational and statistical challenges in the theory still prevent Optimal Transport to be the method of choices in scientific discovery. Unfortunately, several Multi-marginal OT problems of interest suffer from the so-called curse of dimensionality — their computational complexity scales exponentially in the number N of marginals and are NP-hard. In contrast to the N=2 marginals theory, many analytical and geometrical aspects of MOT problems are far from being fully understood.

Faculty Supervisor:

Augusto Gerolin

Student:

Partner:

Kyiv School of Economics

Discipline:

Mathematics

Sector:

Education

University:

University of Ottawa

Program: