Thematic Program on Geometric Analysis and Spectral Theory

这笔赠款将为大约65名年轻的美国人提供旅费。2012年1月至7月，在“几何分析和谱理论专题方案”期间，研究人员参加蒙特利尔数学研究中心的讲习班，第一次几何偏微分方程讲习班将于2012年4月23日至27日举行。英文名称：Geometry and Dynamics of Fluids（包括稳定性和适定性）* 本征值和本征函数的几何学（包括谱渐近和水平集几何）* 几何PDE（包括Monge-Ampere方程、超曲面流和Ricci流）* 几何和分析中的随机分布/概率方法（包括随机波和指标）此外，鼓励参与者在此期间参加CRM的其他活动，包括预备小型课程和特别讲座。许多以前的主题方案的程序已与AMS合作出版，许多发言者和参与者预计将来自美国这笔赠款将资助约65美元的差旅费。2012年上半年，在蒙特利尔举办了一个数学领域的研讨会。这四个研讨会都属于将弯曲空间的几何与模拟物理问题（如流体，热和引力）的微分方程相关联的总主题。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决方案是最著名的例子。一般来说，CRM（Centre de Recherches Mathematiques）每年都会举办一到两个这样的主题课程，吸引来自加拿大，美国和世界其他地区的数学家。参加这样的国际研讨会是数学家了解最新研究项目并开始富有成效的合作的绝佳方式，而像这样的NSF赠款资金通常是美国数学家参加这样的会议的唯一途径（即使他/她正在做演讲）。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/