Geometric Analysis and Nonlinear Elliptic PDE's

我们将于2006年10月27日、28日和29日在马里兰州巴尔的摩市的约翰霍普金斯大学召开一次会议，将几何和非线性椭圆偏微分方程领域的顶尖研究人员、研究生和博士后聚集在一起。几何与非线性椭圆偏微分方程之间的丰富联系在历史上导致了各自的许多突破。通过将这两个领域的顶尖人士聚集在一起，我们希望既能促进进一步的互动，又能向博士后和研究生介绍一些关键的想法和联系。组织者希望这次会议能够促进几何和微分方程之间的互动，特别是向年轻的数学家介绍这两种技术。以下嘉宾接受了我们的演讲邀请：Luis Caffarelli， Daniela Desilva， L. Craig Evans, David Jerison, Fanghua Lin, William H. Meeks III和Richard M. Schoen。偏微分方程（PDEs）在许多科学和数学领域发挥着关键作用，并且已经开发了许多强大的技术来研究它们。偏微分方程在研究弯曲（即非平坦）空间的微分几何的一些关键进展中也发挥了重要作用。事实上，如果没有微分几何的语言，一些重要的偏微分方程就不能恰当地表述（爱因斯坦在广义相对论中的方程就是这样一个例子）。在几何学中出现的偏微分方程通常是高度非线性的，需要新的技术来解决，这对几何学家和分析人员都提出了新的挑战。其中一些为几何偏微分方程开发的新技术已导致其他偏微分方程的重要发展。通过将这两个领域的顶尖专家聚集在一起，我们希望鼓励这些密切相关领域之间的思想交流，并让年轻的数学家接触到这两个领域的技术。

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.