Topics in Optimal Transportation (Graduate Studies in Mathematics, Vol. 58)
(This is the first comprehensive introduction to the theor...)
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.
In 1781, Gaspard Monge defined the problem of "optimal transportation" (or the transferring of mass with the least possible amount of work), with applications to engineering in mind. In 1942, Leonid Kantorovich applied the newborn machinery of linear programming to Monge's problem, with applications to economics in mind. In 1987, Yann Brenier used optimal transportation to prove a new projection theorem on the set of measure preserving maps, with applications to fluid mechanics in mind.
Each of these contributions marked the beginning of a whole mathematical theory, with many unexpected ramifications. Nowadays, the Monge-Kantorovich problem is used and studied by researchers from extremely diverse horizons, including probability theory, functional analysis, isoperimetry, partial differential equations, and even meteorology.
Originating from a graduate course, the present volume is intended for graduate students and researchers, covering both theory and applications. Readers are only assumed to be familiar with the basics of measure theory and functional analysis.
Cédric Villani, French mathematician, educator. Recipient Louis Armand prize, French Academy of Sciences, 2001, Jacques Herbrand prize, 2007, Peccot-Vimont prize, Collège de France, 2003, European Mathematics Society prize, 2008, Henri Poincaré prize, International Association Mathematics Physics, 2009, Fermat prize, Toulouse Mathematics Institute, France, 2009, Fields medal, International Mathematics Union, 2010.
Background
Villani, Cédric was born on October 5, 1973 in Brive-la-Gaillarde, France.
Education
Graduate, École Normale Supérieure (École Normale Supérieure), Paris, 1996. Doctor of Philosophy, École Normale Supérieure (École Normale Supérieure), Paris, 1998.
Career
Professor École Normale Supérieure de Lyon, since 2000. Director Institut Henri Poincaré, Paris, since 2009. Visiting professor Georgia Institute of Technology, Atlanta, 1999.
Miller visiting research professor University California, Berkeley, 2004. Member Institute Advanced Study, Princeton, New Jersey, 2009.
Recipient Louis Armand prize, French Academy ofRecipient Louis Armand prize, French Academy of Sciences, 2001, Jacques Herbrand prize, 2007, Peccot-Vimont prize, Collège de France, 2003, European Mathematics Society prize, 2008, Henri Poincaré prize, International Association Mathematics Physics, 2009, Fermat prize, Toulouse Mathematics Institute, France, 2009, Fields medal, International Mathematics Union, 2010.