Organizer: Alice Chang (Princeton University)

The special program for the academic year 2008-09 will be on geometric PDE.

The emphasis will be on non-linear partial differential equations with

applications to problems in differential, conformal and convex geometry.

Topics that will be covered include Yamabe type equations, Q-curvature

equations, fully non-linear equations in conformal and convex geometry,

construction of conformal invariants and operators, problems in conformally

compact Einstein manifolds, measure and probability theory approaches to the

Ricci tensor.

Partial differential equations continue to be one of the central tools for

studying geometric and even topological questions, and one goal of this

program will be to bring researchers in geometry and PDE together to study

problems of common interest in areas such as those mentioned above.

There will be mini-courses at the beginning of each term and workshops

during the terms.

**Mini-courses: (Simonyi Hall Seminar Room)**

Matthew Gursky, Fully Nonlinear Equations in Conformal Geometry, October 7,14,21 and 28 from 1:30 pm - 3:30 pm.

Andrea Malchiodi, Variational techniques for the prescribed $Q$-curvature equation, October 21 and 28 from 1:30 pm - 3:30 pm.

Neil Trudinger, Optimal transportation and nonlinear elliptic PDE, November 11 and 18 from 1:30 pm - 3:30 pm.

Luis Caffarelli, Issues in Homogenization for Problems with Nondivergence Structure, January 15 and 22 from 2:00 pm - 3:00 pm.

The program will be led by Alice Chang of Princeton University who will be

in residence at the Institute for the academic year. Luis Caffarelli of The University of Texas at Austin will be in residence during term II of the program.

The Institute for Advanced Study is an Equal Opportunity/Affirmative Action

Employer and encourages applications from women, minorities and postdoctoral

researchers.