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A partial differential equation (PDE) is fully nonlinear if it is nonlinear with respect to the highest order derivatives. Fully nonlinear PDEs arise in many different areas in geometry and physics. The most well-known examples are the Monge-Ampere equation, which relates to curvature problems in geometry, and the Bellman equation, which arises in stochastic control theory. The study of fully nonlinear PDEs has been a very active area in the last two decades and remarkable advances have been made. This program will emphasize recent new developments in this field.

The 2005 programme will consists of short lecture series and research seminars in the first two weeks, and a workshop in the last week. Lectures series will cover topics including regularity and variational properties for the Hessian and curvature equations, fully nonlinear version of the Yamabe problem in conformal geometry, regularity of the Monge-Ampere equation and applications to the Bernstein and Plateau problems for the affine maximal surface equation, and the optimal transportation problem.

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