Geometric Analysis and Nonlinear Elliptic PDE's

几何分析和非线性椭圆偏微分方程

• 批准号: 0623843
• 负责人: William Minicozzi
• 金额: $ 1.95万
• 依托单位: Johns Hopkins University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-07-01 至 2008-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0623843&HistoricalAwards=false
• 关键词: Geometric; Analysis; Nonlinear; Elliptic; PDE

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.

我们将在2006年10月27日，28日和29日在马里兰州巴尔的摩的约翰霍普金斯大学举行的会议上，将顶级研究人员以及研究生和研究生汇集到几何和非线性椭圆形偏微分方程中。 在将这两个领域的顶级人士汇集在一起​​时，我们希望既刺激进一步的互动，又将研究生和研究生介绍给一些关键思想和联系。 组织者希望会议将刺激几何与PDE之间的相互作用，尤其是向年轻的数学家介绍两者的技术。 以下内容接受了我们发言的邀请：路易斯·卡法雷利（Luis Caffarelli），丹妮拉·德西尔瓦（Daniela Desilva），莱格·克雷格·埃文斯（L.部分微分方程（PDE）在许多科学和数学领域都起着关键作用，并且已经开发了许多强大的技术来研究它们。 部分微分方程在差异几何形状的某些关键进展中也起着重要作用，其中一项研究弯曲了（即不是平坦的）空间。 实际上，如果没有差异几何形状的语言，就无法正确说明某些重要的PDE（Einstein的方程式中的方程式提供了一个这样的例子）。 几何形状中出现的PDE通常是高度非线性的，需要新技术来解决，并向几何学家和分析师提出了新的挑战。 这些用于几何PDE开发的新技术中有一些为其他PDE提供了重要的发展。 通过将这两个领域的高级专家汇集在一起​​，我们希望鼓励在这些密切相关的领域之间交流思想，并使年轻的数学家将两者的技术揭露。