U.S.-France Cooperative Research: Higher Order Elliptic Equations in Geometry

这项为期三年的美法几何学合作奖包括印第安纳大学的Matthew L. Gursky，普林斯顿大学的Paul C. Yang和Sung-Yung Chang，塞尔日-蓬图瓦兹大学的Frank Merle和Emmanuel Hebey。该合作涉及几何和数学物理中的高阶椭圆方程，特别是四阶方程和抛物方程。这些几何问题出现在共形几何、爱因斯坦流形和规范度量中。美国数学家为这次合作带来了高阶方程的专业知识。法国在分析问题方面的专门知识补充了这一点。该奖项代表了美国方面向美国国家科学基金会和法国国家科学研究中心（CNRS）联合提出的建议。美国国家科学基金会将支付美国研究人员和学生的个人访问和团体旅行到研讨会的旅费和生活费。CNRS将支持法国研究人员的访问。该合作将促进对应用于物理、几何和分析问题的高阶方程的基本理解。该项目为学生培训增加了国际层面，并提供了发展国际伙伴关系的机会。

0129266GurskyThis three-year award for U.S.-France collaboration in geometry involves Matthew L. Gursky at Indiana University, Paul C. Yang and Sung-Yung Chang at Princeton University, Frank Merle and Emmanuel Hebey at the University of Cergy-Pontoise. The collaboration addresses higher order elliptic, in particular fourth order, and parabolic equations in geometry and mathematical physics. These geometry problems arise in conformal geometry, Einstein manifolds, and canonical metrics. The US mathematicians bring to this collaboration expertise in higher order equations. This is complemented by French expertise in analytical problems.This award represents the US side of joint proposals to the NSF and the French National Center for Scientific Research (CNRS). NSF will cover travel funds and living expenses for individual visits of US investigators and students and group travel to a workshop. The CNRS will support the visits of the French researchers. The collaboration will advance fundamental understanding of higher order equations as applied to problems in physics, geometry, and analysis. The project adds an international dimension to training of students and provides opportunities to develop international partnerships.