Overview

The theory of optimal transportation has its origins in the eighteenth century when the problem of transporting resources at a minimal cost was first formalised. Through subsequent developments, particularly in recent decades, it has become a powerful modern theory. This book contains the proceedings of the summer school 'Optimal Transportation: Theory and Applications' held at the Fourier Institute in Grenoble. The event brought together mathematicians from pure and applied mathematics, astrophysics, economics and computer science. Part I of this book is devoted to introductory lecture notes accessible to graduate students, while Part II contains research papers. Together, they represent a valuable resource on both fundamental and advanced aspects of optimal transportation, its applications, and its interactions with analysis, geometry, PDE and probability, urban planning and economics. Topics covered include Ricci flow, the Euler equations, functional inequalities, curvature-dimension conditions, and traffic congestion.

Full Product Details

Author:   Yann Ollivier (Université de Paris XI) ,  Hervé Pajot (Université de Grenoble) ,  Cedric Villani (Université de Paris VI (Pierre et Marie Curie))
Publisher:   Cambridge University Press
Imprint:   Cambridge University Press
Volume:   413
Dimensions:   Width: 15.20cm , Height: 1.80cm , Length: 22.80cm
Weight:   0.470kg
ISBN:  

9781107689497

ISBN 10:   110768949
Pages:   316
Publication Date:   07 August 2014
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
We will order this item for you from a manufactured on demand supplier.

Table of Contents

Part I. Short Courses: 1. Introduction to optimal transport theory Filippo Santambroggio; 2. Models and applications of optimal transport in economics, traffic and urban planning Filippo Santambroggio; 3. Logarithmic Sobolev inequality for diffusions and curvature-dimension condition Ivan Gentil; 4. Lecture notes on variational methods for incompressible Euler equations Luigi Ambrosio and Alessio Figalli; 5. Ricci flow: the foundations via optimal transportation Peter Topping; 6. Lecture notes on gradient flows and optimal transport Sara Danieri and Guiseppe Savare; 7. Ricci curvature, entropy, and optimal transport Shin-Ichi Ohta; Part II. Survey and Research Papers: 8. Computing the time-continuous optimal mass transport without Lagrangian techniques Olivier Besson, Martine Picq and Jérome Poussin; 9. On the duality theory for the Monge–Kantorovich transport problem Mathias Beiglbock, Chrsitian Léonard and Walter Schachermayer; 10. Optimal coupling for mean field limits François Bolley; 11. Functional inequalities via Lyapunov conditions Patrick Cattiaux and Arnaud Guillin; 12. Size of the medial axis and stability of Federer's curvature measures Quentin Mérigot.

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Author Information

Hervé Pajot has been a full professor at the Fourier Institute (University of Grenoble) since 2003. He is the author of Analytic Capacity, Rectifiability, Menger Curvature and the Cauchy Integral, considered a standard reference in the subject. He is currently chief editor of the Annales de l'Institut Fourier. Yann Ollivier is a research scientist at the CNRS, Paris-Sud (Saclay) University, France. His research focusses on various areas of pure and applied mathematics, always featuring a strong interaction between geometric and probabilistic aspects, such as the geometry of random groups, the curvature of Markov chains on metric spaces, statistical viewpoints on general relativity, or the mathematics of artificial intelligence. He is the recipient of several prizes, including the Bronze Medal of the CNRS. Cedric Villani is the director of the Institut Henri Poincaré, Paris, and a professor at the University of Lyon. He is the author of two books on optimal transport, and was awarded the Fields medal at the 2010 International Congress of Mathematicians in Hyderabad. He often serves as a spokesman for the French mathematical community.

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