# Geometric Partial Differential Equations

Organizer: Alice Chang (Princeton University)

The special program for the academic year 2008-09 was on geometric PDE. The emphasis was on non-linear partial differential equations with applications to problems in differential, conformal and convex geometry. Topics 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 were 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 was led by Alice Chang of Princeton University who was in residence at the Institute for the academic year. Luis Caffarelli of The University of Texas at Austin was in residence during term II of the program.

10 Year Impact Statement

The Institute for Advanced Study is an Equal Opportunity/Affirmative Action Employer and encourages applications from women, minorities and postdoctoral researchers.

### Date & Time

September 01, 2008 | 12:00am – June 30, 2009 | 12:00am