Optimal Transport: Old and New

by Cédric Villani

At the close of the 1980s, the independent contributions of Yann Brenier, Mike Cullen and John Mather launched a revolution in the venerable field of optimal transport founded by G. Monge in the 18th century, which has made breathtaking forays into various other domains of mathematics ever since. The author presents a broad overview of this area, supplying complete and self-contained proofs of all the fundamental results of the theory of optimal transport at the appropriate level of generality. Thus, the book encompasses the broad spectrum ranging from basic theory to the most recent research results. PhD students or researchers can read the entire book without any prior knowledge of the field. A comprehensive bibliography with notes that extensively discuss the existing literature underlines the book’s value as a most welcome reference text on this subject.

Genres: Mathematics

998 pages, Hardcover

First published November 1, 2008

About the author

Cédric Villani is a French mathematician who has received many international awards for his work including the Jacques Herbrand Prize, the Prize of the European Mathematical Society, the Fermat Prize and the Henri Poincaré Prize.

In 2010 he was awarded the Fields Medal, the International Medal for Outstanding Discoveries in Mathematics, for his work on Landau damping and the Boltzmann equation. Often called ‘the mathematicians’ Nobel Prize’, it is awarded every four years and is viewed by some as the highest honour a mathematician can achieve.

He is a professor at Lyon University and Director of the Institut Henri Poincaré in Paris, working primarily on partial differential equations and mathematical physics.

Reviews

[Matthew Zhang · Rating 3 out of 5]

extremely dense book