Thematic Program on Geometric Analysis and Spectral Theory

点击翻译按钮获取中文摘要

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/