Optimal Transport

March 10 - June 13, 2008

Overview

The general problem of irrigation and transportation in physics and biology is to transport in the most economical way a source mass distribution onto a fixed well distribution. Both source and wells distributions are usually modeled as positive measures in a Cartesian space or in a metric space. This problem can be looked at as a generalization of the optimal assignment or the optimal flow problem in operational research, in which case the subjacent space is a fixed graph. In the new more general setting, the irrigation network is itself an unknown of the problem. The examples are manifold: lungs, blood vessels, irrigation or draining networks, natural or artificial. On the side of urban optimization, the question ranges from the optimization of the supply networks (power, water, wires) to the public transportation and traffic optimization problem. The simplest and more noble and antique version of the problem is the Monge-Kantorovich problem, where the cost assigned to transportation is just an increasing function of distance. Fluid mechanics arguments have to be added as soon as the transportation network is optimized with a flow-dependent cost as is natural in most of the above mentioned situation: the thicker the vessel, the road, the channel, the wire etc., the cheaper the transportation.

The aim of the workshop is to put together physicists, biologists, mathematicians working on the optimization of transportation networks.

Organizing Committee

Andrea Bertozzi (University of California, Los Angeles (UCLA), Mathematics)
Yann Brenier (Université de Nice Sophia Antipolis)
Jose Carrillo (Autonomous University of Barcelona, ICREA)
Wilfrid Gangbo (Georgia Institute of Technology)
Peter Markowich (University of Cambridge, Department of Applied Mathematics and Theoretical Physics)
Jean-Michel Morel (École Normale Supérieure de Cachan, CMLA)