Two books about optimal transportation by Cédric Villani

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.


After attending the Lycée Louis-le-Grand, Villani was admitted to the école normale supérieure in Paris and studied there from 1992 to 1996. He was later appointed assistant professor in the same school. He received his doctorate at Paris-Dauphine University in 1998, under the supervision of Pierre-Louis Lions, and became professor at the école normale supérieure de Lyon in 2000. He is now professor at Lyon University. He has been the director of Institut Henri Poincaré in Paris since 2009. Prizes: 2001: Louis Armand Prize of the Academy of Sciences 2003: Peccot-Vimont Prize and Cours Peccot of the Collège de France 2007: Jacques Herbrand Prize (French Academy of Sciences) 2008: Prize of the European Mathematical Society 2009: Henri Poincaré Prize 2009: Fermat Prize 2010: Fields Medal 2014: Joseph L. Doob Prize of the American Mathematical Society for his book [Optimal Transport: Old and New (Springer 2009)] Extra-academic distinctions: 2009: Knight of the National Order of Merit (France) 2011: Knight of the Legion of Honor (France) 2013: Member of the French Academy of Sciences


From the reviews: "The book is aimed to old and new problems of optimal transport. … This meticulous work is based on very large bibliography … that is converted into a very valuable monograph that presents many statements and theorems written specifically for this approach, complete and self-contained proofs of the most important results, and extensive bibliographical notes." (Mihail Voicu, Zentralblatt MATH, Vol. 1156, 2009) “This book wins the challenge to give a new and broad perspective on the multifacet topic of the optimal mass transport. … Besides extensive and accurate references therein the reader will find comments on related questions barely touched upon in the main text as well as lively presentations on how ideas and results have developed. This book should prove useful both to the expert and to the beginner looking for a reference text on the subject.” (Dario Cordero Erausquin, Mathematical Reviews, Issue 2010 f) “The book is an in-depth, modern, clear exposition of the advanced theory of optimal transport, and it tries to put together in a unified way almost all the recent developments of the theory. … the book is extremely well written and very pleasant to read. … I strongly recommend this excellent book to every researcher or graduate student in the field of optimal transport. … of interest to many mathematicians in different areas, who are simply interested in having an overview of the subject.” (Alessio Figalli, Bulletin of the American Mathematical Society, Vol. 47 (4), February, 2010)



Topics in Optimal Transportation
by Cédric Villani


This is the first comprehensive introduction to the theory of mass transportation with its many—and sometimes unexpected—applications. In a novel approach to the subject, the book both surveys the topic and includes a chapter of problems, making it a particularly useful graduate textbook.