Thematic Program on Geometric Analysis and Spectral Theory

这笔赠款将资助约65名年轻的美国研究人员参加2012年1月至7月期间在蒙特利尔数学研究中心举办的“几何分析和谱论专题计划”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。研讨会主题为：*流体的几何和动力学(包括稳定性和适定性)*本征值和特征函数的几何(包括谱渐近和水平集几何)*几何偏微分方程组(包括Monge-Ampere方程、超曲面流动、和Ricci Flow)*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，还鼓励参与者在此期间参加CRM的其他活动，包括预备迷你课程和专题讲座。许多以前的主题项目的会议记录都是与AMS合作出版的，预计许多演讲者和参与者将来自美国。这笔赠款将为2012年上半年在蒙特利尔参加其领域研讨会的约65名处于职业生涯早期的美国数学家提供旅费。这四个工作坊的总主题都是将弯曲空间的几何与为物理学(如流体、热量和引力)中的问题建模的微分方程式联系起来。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·佩雷尔曼对庞加莱猜想的解是最著名的例子。一般来说，CRM(研究数学中心)每年都会举办一到两个这样的主题项目，它们吸引了来自加拿大、美国和世界其他地方的数学家。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方式，而像这样来自美国国家科学基金会拨款的资金往往是初出茅庐的美国数学家参加这样的会议的唯一途径(即使是在做演讲)。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/