This three week program will emphasize the overlapping research areas of nonlinear dispersive equations (NDE) and nonlinear elliptic equations (NEE), and is intended as an extension of the MSRI programs in these fields from Fall, 2005, with a focus on subsequent research developments. Weeks 1 and 3 will comprise informal but focused workshops on NEE and NDE, respectively. Topics of emphasis will include regularity estimates for elliptic PDE, with applications to mass transport problems and to image processing. The NDE workshop will focus upon eigenfunction estimates, resonances and spectral resolutions for elliptic operators on manifolds. Week 2 will be devoted to several expository minicourses, of general interest, especially for younger mathematicians. We are currently planning these lecture series:

• Craig Evans, "Survey of weak convergence methods for nonlinear PDE'"
• Cristian Gutierrez, "The Monge-Ampere equation''
• Chris Sogge, "Dispersion and existence theorems for nonlinear wave equations"
• Daniel Tataru, "Nonlinear wave equations''

A block of rooms has been reserved at the Hotel Durant. Please mention the workshop name and reference the following code when making reservations via phone, fax or e-mail: TQ0000. The cut-off date for reservations is Jun 22, 2007.