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Summer school 2019

A NUMERICAL INTRODUCTION TO OPTIMAL TRANSPORT

Optimal Mass Transportation is a mathematical research topic which started two centuries ago with Monge’s work on the “Th ́eorie des d ́eblais et des remblais” This engineering problem consists in minimizing the transport cost between two given mass densities.

  • Date : 13/05/2019 to 17/05/2019
  • Place : Inria de Paris, 2 rue Simone Iff, 75012 Paris

In the 40’s, Kantorovich in- troduced a powerful linear relaxation and introduced its dual formulation. The Monge-Kantorovich problem became a specialized research topic in opti- mization and Kantorovich obtained the 1975 Nobel prize in economics for his contributions to resource allocations problems.

 Since the seminal discoveries of Brenier in the 90’s, Optimal Transportation has received renewed atten- tion from mathematical analysts with two recent fields Medal awarded Villani (2010) and Figalli (2018). Optimal Mass Transportation is today a mature area of mathematical analysis with a constantly growing range of applica- tions.

Optimal Transportation and the associated Wassertein distance for densities has also received a lot of attention from probabilists. The research and development of numerical methods for Optimal Transportation and Op- timal Transportation related problems has gained significant momentum in the last 5 years and several class of methods have been or are currently applied in diverse applications fields : astropysics, satellite data analysis, freeform optics, academic fluid models, crowd motion ... Three new books by F. Santambrogio ( “Optimal Transportation for applied mathematicans” ), A. Galichon (“Optimal Transport in Economics”) and Peyr ́e / Cuturi (“ Computational Optimal Transport”) have been published since 2015.

Summer schools are intended for researchers, engineers and PhD students. They allow them to review the state of progress of the proposed subjects and to confront their experience. The teaching is done in English. It is complemented by practical works, hosted by assistants.

Keywords: Numerical Analysis Summer school 2019 India de Paris Optimal transport

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