Linear and nonlinear elliptic and parabolic partial differential equations have been deliberated by continuous, discrete, and computational methods. There are deep connections between the geometry and analysis of Riemannian and Kähler manifolds. The topics of function theory and the analysis of the Laplace and heat equations on manifolds include harmonic function theory on complete Riemannian manifolds, the spectrum of the Laplacian operator, spaces of holomorphic functions on complete Kähler manifolds, partial differential equations on complete manifolds and their relation with the geometry of complete Riemannian and Kähler manifolds. Nonlinear elliptic and parabolic methods in geometry and analysis to be considered include Kähler-Einstein metrics, Yamabe problem, and the porous medium equation. Schedule: Monday, October 23   9:30 - 10:30 Andrejs Treibergs: An Eigenvalue Estimate and a Capture Problem 10:30 - 11:00 Morning Break 11:00 - 12:00 Simon Brendle: Boundary regularity of minimal maps 12:00 -   2:00 Lunch   2:00 -   3:00 Sophie Chen: Boundary estimates for generalized Yamabe equations Tuesday, October 24 10:30 - 11:30 Peter Topping: Ricci flow, entropy and optimal transportation 11:30 -   2:00 Lunch   2:00 -   3:00 Richard Schoen: Sharp isoperimetric inequalities for minimal surfaces   3:00 -   3:30 Afternoon Break   3:30 -   4:30 Gerhard Huisken: An isoperimetric concept for mass and quasilocal mass via surface flows   4:30 -   5:30 Reception Wednesday, October 25   9:30 - 10:30 Alexander Grigor'yan: Heat kernels on weighted manifolds and applications 10:30 - 11:00 Morning Break 11:00 - 12:00 Christoph Böhm: Manifolds with positive curvature operators are space forms Thursday, October 26 10:30 - 11:30 Lei Ni: Kähler-Ricci solitons and holomorphic functions of polynomial growth 11:30 -   2:00 Lunch   2:00 -   3:00 Duong Phong: The degenerate complex Monge-Ampere equation and Donaldson geodesics Friday, October 27   9:30 - 10:30 Zhiqin Lu: On the Chern classes of CY moduli 10:30 - 11:00 Morning Break 11:00 - 12:00 Leon Simon: An interior gradient estimate for solutions of the symmetric minimal surface equation 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: K30000. The cut-off date for reservations is September 22, 2006. A block of rooms has been reserved at the Rose Garden Inn. Reservations may be made by calling 1-800-992-9005 OR directly on their website. Click on Corporate at the bottom of the screen and when prompted enter code MATH (this code is not case sensitive). By using this code a new calendar will appear and will show MSRI rate on all room types available. The following Group Code should be entered in the "Comment" field when booking through our Website. Group Code = CGMS34. Please note: The Original Queen room type does not have an in-room T1 connection, but we do have WIFI available in our main lobby area. The cut-off date for reservations is September 26, 2006.