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Look Inside Optimal Transport

Optimal Transport
Theory and Applications

Part of London Mathematical Society Lecture Note Series

Editors:
Yann Ollivier, Université de Paris XI
Hervé Pajot, Université de Grenoble
Cedric Villani, Université de Paris VI (Pierre et Marie Curie)

Filippo Santambroggio, Ivan Gentil, Luigi Ambrosio, Alessio Figalli, Peter Topping, Sara Danieri, Guiseppe Savare, Shin-Ichi Ohta, Olivier Besson, Martine Picq, Jérome Poussin, Mathias Beiglbock, Chrsitian Léonard, Walter Schachermayer, François Bolley, Patrick Cattiaux, Arnaud Guillin, Quentin Mérigot

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Date Published: August 2014
availability: Available
format: Paperback
isbn: 9781107689497

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Description

Contents

Resources

Courses

About the Authors

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.
- Contains short courses which give an accessible introduction to problems of current interest, and research papers which present modern developments
- The book presents both the theory of optimal transport and some of its many applications
- Of interest to researchers in pure and applied mathematics, physics, computer science and economics
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Product details
- Date Published: August 2014
- format: Paperback
- isbn: 9781107689497
- length: 316 pages
- dimensions: 228 x 152 x 18 mm
- weight: 0.47kg
- availability: Available
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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Editors
Yann Ollivier, Université de Paris XI
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.
Hervé Pajot, Université de Grenoble
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, Université de Paris VI (Pierre et Marie Curie)
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.
Contributors
Filippo Santambroggio, Ivan Gentil, Luigi Ambrosio, Alessio Figalli, Peter Topping, Sara Danieri, Guiseppe Savare, Shin-Ichi Ohta, Olivier Besson, Martine Picq, Jérome Poussin, Mathias Beiglbock, Chrsitian Léonard, Walter Schachermayer, François Bolley, Patrick Cattiaux, Arnaud Guillin, Quentin Mérigot