Thematic Program on Geometric Analysis and Spectral Theory

该基金将资助约65名年轻的美国研究人员于2012年1月至7月在蒙特利尔数学研究中心参加“几何分析和光谱理论专题项目”的研讨会，其中第一次几何偏微分方程研讨会将于2012年4月23日至27日举行。获资助的工作坊主题包括：*本征值和本征函数的几何（包括谱渐近性和水平集的几何）*几何偏微分方程（包括蒙日-安培方程、超表面流和里奇流）*几何和分析中的随机度量/概率方法（包括随机波和度量）此外，鼓励参与者在此期间参加CRM的其他活动。包括预备课程和专题讲座。以前许多专题项目的论文集已经与AMS合作出版，许多演讲者和参与者预计将来自美国。这笔资助将资助约65名美国数学家的旅费，他们将在2012年上半年参加在蒙特利尔举行的他们领域的研讨会。这四个讲习班的主题都是将弯曲空间的几何与模拟物理问题（如流体、热和引力）的微分方程联系起来。在过去的10-20年里，这种关系一直是数学中最活跃的研究领域之一，格里戈里·佩雷尔曼（Grigory Perelman）对庞加莱猜想的解答是最著名的例子。一般来说，CRM （Centre de Recherches Mathematiques）每年都会举办一到两个这样的主题项目，吸引来自加拿大、美国和世界各地的数学家。对于数学家来说，参加这样的国际研讨会是了解最新研究项目并开始富有成效的合作的绝佳途径，而来自美国国家科学基金会（NSF）的资助通常是美国数学家参加这样的会议的唯一途径（即使他/她是在做演讲）。http://www.crm.umontreal.ca/Analysis2012/index.php/

This grant will fund travel expenses for about 65 young U.S.-based researchers to attend workshops at the Centre de Recherches Mathematiques in Montreal between January and July 2012, during the "Thematic Program on Geometric Analysis and Spectral Theory," with the first workshop on Geometric Partial Differential Equations taking place on April 23-27 2012.The workshop topics to be funded are: * Geometry and Dynamics of Fluids (including stability and well-posedness)* Geometry of Eigenvalues and Eigenfunctions (including spectral asymptotics and geometry of level sets)* Geometric PDE (including the Monge-Ampere equations, hypersurface flows, and Ricci flow)* Random Metrics/Probabilistic Methods in Geometry and Analysis (including random waves and metrics) In addition, participants are encouraged to attend other events at the CRM during this time, including preparatory minicourses and special lectures. Proceedings of many previous thematic programs have been published in collaboration with the AMS, and many of the speakers and participants are expected to be from the U.S.This grant will fund travel expenses for about 65 U.S.-based mathematicians who are early in their careers to attend a workshop in their field in Montreal during the first half of 2012. The four workshops all fall under the general theme of relating the geometry of curved spaces to the differential equations that model problems in physics (such as fluids, heat, and gravitation). In the last 10-20 years, this relationship has been one of the most active research areas of mathematics, with Grigory Perelman's solution of the Poincare Conjecture being the most well-known instance. Generally the CRM (Centre de Recherches Mathematiques) hosts one or two of these themed programs per year, and they attract mathematicians from all over Canada, the United States, and the rest of the world. Attending such an international workshop is an excellent way for a mathematician to learn about the latest research projects and start productive collaborations, and funds from NSF grants like this are often the only way for a beginning American mathematician to attend a conference like this (even if s/he is giving a talk). http://www.crm.umontreal.ca/Analysis2012/index.php/