Topics in Optimal Transportation (Graduate Studies in Mathematics, 58) - Softcover

Cédric Villani

Softcover

ISBN 10: 1470467267 ISBN 13: 9781470467265

Publisher: American Mathematical Society, 2021

Synopsis

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.

About this title

About the Author

Cédric Villani: École Normale Supérieure de Lyon, Lyon, France

Edition details

• Publisher: American Mathematical Society
• Publication date: 2021
• Language: English
• ISBN 10: 1470467267
• ISBN 13: 9781470467265
• Binding: Paperback
• Number of pages: 370