Pacific Institute for the Mathematical Sciences - PIMS

Optimal Transport theory emerged more than two centuries ago as an engineering problem posed by Gaspard Monge just before the French revolution. Its rich mathematical structure was first revealed by the Russian Nobel-prize winner Kantorovich during world War II, and then about 30 years ago by Yann Brenier in his work on fluid dynamics, Robert McCann in his forays in mathematical physics, and by Wilfrid Gangbo and Craig Evans who, using PDE methods, eventually solved the original problem of Monge. Many other breakthroughs followed, led by Luigi Ambrosio, Felix Otto and their schools leading to the recent Fields medals for Cedric Villani and Alessio Figalli.

The richness of the theory of optimal transportation stems from its central role in many branches of mathematics, be them theoretical, applied or computational. Indeed, the basic problem of transporting a probability measure onto another probability measure, while minimizing a given cost of the transport, is now at the core of a wide range of problems in mathematics, physics, economics, statistics, computer science, biology and neuroscience. Recent theoretical and computational advances have paved the way for major breakthroughs in all these areas.

The theory of optimal mass transport has had an impact on various classical branches of mathematics: geometry, analysis, dynamics, partial differential equations, and
uid mechanics. Since it defines a distance between very general distributions and entities of various nature, essential for object recognition and classification, it is now widely investigated in signal processing, machine learning, weather prediction, neuroscience, computer vision, and astrophysics.

Organized by the Center for Advanced Mathematical Sciences and the Pacific Institute for the Mathematical Sciences , the goal of this mini-school is to introduce graduate and senior undergraduate students to the basic theory, but also to many of its applications and to recent breakthroughs. The symposium, which is supported by the Kantorovich Initiative will provide an environment that will facilitate interactions between experts, identify new challenges, and help jumpstart collaborative work.

Mini-courses

1. Introductory course on OT, Brendan Pass (U. of Alberta)

2. Numerical methods in OT, Quentin Merigot (U. Orsay)

3. Stochastic OT and Finance, Walter Schachermayer (U. Vienna)

4. OT in Physics and Cosmology, Yann Brenier (CNRS)

Confirmed participants

Ivar Ekeland, Dauphine

Guillaume Carlier, U. Dauphine

Wilfrid Gangbo, UCLA

Nassif Ghoussoub, UBC

Robert McCann, U. Toronto

Soumik Pal, U. Washington

Young-Heon Kim, UBC

Bernard Dacorogna, EPFL

Luigi De Pascale,

Nicolas Juillet,

Omar Abdul Halim, U. Alberta (grad student)

Alfred Galichon, New York University

Diogo Aguiar Gomes, KAUST

Nizar Touzi, Polytechnique

Beiglbck, Mathias (University of Vienna)

Jose A. Carrillo, University of Oxford,

Craig Cowan, U. Manitoba

Samer Dweik, Lebanon

Jean-David Benamou, INRIA

Lavenant Hugo, Bocconi University

Lim, Tongseok, Purdue University

Location: American University of Beirut, Lebanon

For more information on this event please email Hiba Hammoud.