We will bring together top researchers, as well as graduate students and post-docs, in both geometry and nonlinear elliptic partial differential equations for a conference at the Johns Hopkins University in Baltimore, MD, on October 27, 28, and 29 in 2006. The rich connections between geometry and non-linear elliptic partial differential equations have historically led to many breakthroughs in each. In bringing together top people in both areas, we hope both to stimulate further interaction and to introduce post-docs and graduate students to some of the key ideas and connections. The organizers hope that the meeting will stimulate the interaction between geometry and pde, especially to introduce younger mathematicians to the techniques from both. The following have accepted our invitation to speak: Luis Caffarelli, Daniela Desilva, L. Craig Evans, David Jerison, Fanghua Lin, William H. Meeks III, and Richard M. Schoen.
Partial differential equations (PDEs) play a key role in many areas of science and mathematics and many powerful techniques have been developed to study them. Partial differential equations have also played an important role in some key advances in differential geometry, where one studies curved (i.e., not flat) spaces. In fact, some important PDEs cannot be properly stated without the language of differential geometry (Einstein's equations in general relativity give one such example). The PDEs that arise in geometry are often highly nonlinear and require new techniques to solve, posing new challenges to both geometers and to analysts. Some of these new techniques developed for geometric PDEs have led to important developments for other PDEs. By bringing together top experts in both areas, we hope to encourage the exchange of ideas between these closely related fields and to expose younger mathematicians to techniques in both.
