A branched structure is observable in most practical transportation systems such as draining and irrigation systems, electric power supply systems and natural objects like the blood vessels, the river basins, or the trees. Recent approaches of these transportation networks derive their branched structure from an energy functional whose essential feature is to favor wide routes. Given a flow $s$ in a river, a road, a tube or a wire, the transportation cost per unit length is supposed in these models to be proportional to s^alpha with 0 < alpha < 1.

The aim of these talks is to compare various (actually equivalent) variational models for these phenomena, and to make the usual work: feasibility, existence of weak solutions, regularity, structure properties, subjacent PDE, open problems and their connections to geophysical models of optimal river networks. Among the open problems are the fractal properties of the infinite irrigation trees, and the existence and regularity of river basins.

• Event: Minicourse on "Branched transport theory"; Speakers: Jean Michel Morel and Filippo Santambrogio (ENS Cachan) (2007)

A branched structure is observable in most practical transportation systems such as draining and irrigation systems, electric power supply systems and natural objects like the blood vessels, the river basins, or the trees. Recent approaches of these transportation networks derive their branched structure from an energy functional whose essential feature is to favor wide routes. Given a flow $s$ in a river, a road, a tube or a wire, the transportation cost per unit length is supposed in these models to be proportional to s^alpha with 0 < alpha < 1.

The aim of these talks is to compare various (actually equivalent) variational models for these phenomena, and to make the usual work: feasibility, existence of weak solutions, regularity, structure properties, subjacent PDE, open problems and their connections to geophysical models of optimal river networks. Among the open problems are the fractal properties of the infinite irrigation trees, and the existence and regularity of river basins.

• Event: Minicourse on "Branched transport theory"; Speakers: Jean Michel Morel and Filippo Santambrogio (ENS Cachan) (2007)

A branched structure is observable in most practical transportation systems such as draining and irrigation systems, electric power supply systems and natural objects like the blood vessels, the river basins, or the trees. Recent approaches of these transportation networks derive their branched structure from an energy functional whose essential feature is to favor wide routes. Given a flow $s$ in a river, a road, a tube or a wire, the transportation cost per unit length is supposed in these models to be proportional to s^alpha with 0 < alpha < 1.

The aim of these talks is to compare various (actually equivalent) variational models for these phenomena, and to make the usual work: feasibility, existence of weak solutions, regularity, structure properties, subjacent PDE, open problems and their connections to geophysical models of optimal river networks. Among the open problems are the fractal properties of the infinite irrigation trees, and the existence and regularity of river basins.

• Event: Minicourse on "Branched transport theory"; Speakers: Jean Michel Morel and Filippo Santambrogio (ENS Cachan) (2007)