Workshop

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.