* Thursdays, starting Sept. 11, 2003 - Guest Lecturer: John Urbas (Australian National University & The Fields Institute)
Fully Nonlinear Elliptic PDE: A Graduate Level Introduction

The optimal transportation problem of Monge and Kantorovich is now understood to be a mathematical crossroads, where problems from economics, fluid mechanics, and physics meet geometry and nonlinear PDE. This course gives a survey of these unexpected developments, using variational methods and duality to address free boundary problems, nonlinear elliptic equations (Monge-Ampere), regularity, geometric inequalities with sharp constants, metric and Riemannian geometry of probability measures, nonlinear diffusion, fluid mixing, and atmospheric flows.
References:
C. Villani. Topics in Optimal Transportation. Providence: AMS 2003.
GSM/58 ISBN 0-8218-3312-X $59 ($47 AMS members)