Here we are concerned with the optimal transport of masses from one location to the other, where the optimality depends upon the context. The problems appear in several areas: economics, probaility, optimition, meteorology and computer graphics. In the last decade, researchers discovered strong connections between these equations and nonlinear PDEs, for example, when the cost function is quadratic the optimal transportation is intimately related to the Monge-Ampere equation. The Wasserstein distance appears in the formulation of several results for evoltuion equations arising from optimal transportation.

NOTE: This workshop is to be held at the International House on the UC Berkeley campus, at 2299 Piedmont Avenue, except for the Tuesday session, which will be held at the Lawrence Berkeley National Laboratory. On site registration for the workshop will start at 8:30 AM Monday and end at 3:30 PM Monday.

Preliminary Schedule

Monday, 11/14
9:15-9:30 Welcome to MSRI (at I-HOUSE)
9:30-10:30 Robert McCann: Introduction to optimal transportation: costs I have known and loved
10:30-11:00 Coffee Break
11:00-11:45 Xu-Jia Wang: Regularity of the Monge-Ampere equation
12:00-12:45 John Lott: Optimal transport and nonsmooth geometry
12:45-2:15 Lunch Break
2:15-3:00 Jonathan Mattingly: Spectral gaps and coupling for degenerate stochastic PDEs
3:30-4:00 Tea/Travel Break to 60 Evans Hall, UCB
4:10-5:10 Neil Trudinger: Nonlinear PDE and mass transport (at 60 Evans Hall, UCB)

Tuesday, 11/15 at Lawerence Berkeley National Laboratory (LBNL)
9:30-10:30 Robert McCann: Free boundaries in optimal transport: a Monge-Ampere obstacle problem
10:30-11:00 Coffee Break
11:00-11:45 Yann Brenier: Transportation of currents in two space dimensions and the Euclidean version of the Born-
Infeld equations
12:00-12:45 Luis Caffarelli: Multiple valued solutions to Monge-Ampere equation
12:45-2:45 Lunch Break
2:45-3:30 Albert Fathi: An Introduction to Weak KAM Theory
3:30-4:00 Tea Break
4:00-4:45 Patrick Bernard

Wednesday, 11/16
9:30-10:30 Robert McCann: Geometric inequalities and gradient flows
10:30-11:00 Coffee Break
11:00-11:45 Giuseppe Buttazzo: Path functionals in Wasserstein spaces
12:00-12:45 Truyen Nguyen: On Monge-Ampere type equations arising in optimal transportation problems
12:45-2:45 Lunch Break
2:45-3:30 Adam Oberman: PDE based and variational numerical methods for mass transportation
3:30-4:00 Tea Break
4:00-4:45 Sanjoy Mitter: Path space estimation for nonlinear diffusion processes

Thursday, 11/17
9:30-10:30 Robert McCann: The principle-agent problem and incentive compatibility in microeconomic theory
10:30-11:00 Coffee Break
11:00-11:45 Chris Shannon
12:00-12:45 Luigi Ambrosio: Hamiltonian flows in the space of probability measures
12:45-2:45 Lunch Break
2:45-3:30 Ludger Ruschendorf: Monge--Kantorovich problem and optimal couplings
3:30-4:00 Tea Break
4:00-4:45 Filippo Santambrogio: Transport and concentration problems and applications

Friday, 11/18
9:30-10:30 Robert McCann: Atmospheric modelling: introduction to semi-geostrophy
10:30-11:00 Coffee Break
11:00-11:45 Adrian Tudorascu: On constrained optimization in the Wasserstein metric
12:00-12:45 Diogo Gomes: Stochastic Mather problem revisited
12:45-2:45 Lunch Break
2:45-3:30 Mike Cullen: Some unsolved problems in semi-geostrophic theory
3:30-4:00 Tea Break
4:00-4:45 Alexander Plakhov: Optimal mass transportation and problems of minimal resistance



This workshop will be held at International House Berkeley Monday, Wednesday, Thursday and Friday. The workshop will take place at Lawrence Berkeley National Laboratory on Tuesday, Nov. 15, 2005. Drop-ins will NOT be able to attend the lectures on Tuesday, due to security at LBNL.

Funding

Important