International Conference on Ricci Flow, Paris, France, June 30 - July 4, 2008

摘要奖：DMS-0704193首席研究员：John W.Lott位于巴黎的亨利·庞加莱研究所将于2008年4月至7月举办为期三个月的关于利玛窦流动和利玛窦曲率的项目。作为法国在几何分析领域迅速发展的这一活动的一部分，定于2008年6月30日至7月4日举行的关于Ricci Flow的国际会议将作为三个月的结束。三个学期和会议的主题预计将包括三维流形几何化中的Ricci流，Kaehler-Einstein度量和Kaehler-Ricci流，常标量曲率的度量，四维及更高维度的Ricci流，几何流的分析方面，爱因斯坦度量和几何相对论的最新发展，合成Ricci曲率和Ricci极限空间。这一格局被Perelman在三维流形上的Ricci流的工作所改变，所有这些领域都获得了最近的进展。这个奖项为巴黎会议的美国与会者，特别是毕业生和初级研究人员提供了部分费用支持。研讨会的主题是利玛窦流动及其延伸。几何中的这一微分方程式和技巧因其应用于庞加莱猜想而闻名于世，庞加莱猜想是关于三维球体的拓扑学唯一性，这是数学中最具挑战性的问题之一。这项技术考虑了具有大量度量的单个空间(测量空间中距离的方法)，通过使用每个度量上的Ricci曲率来确定度量演化的方向，该方向可能使度量更对称--松散地说，我们试图改变度量的方向。尽管通常很难控制使这种论证成功的所有必要的细节，但几何学家已经发现，这个想法在各种重要情况下确定了最佳度量。会议网页ishttp://www.ihp.jussieu.fr/ceb/Trimestres/T08-2/C2/index.html.

AbstractAward: DMS-0704193 Principal Investigator: John W. LottThe Institut Henri Poincare (IHP) in Paris will host atrimester-long program on Ricci Flow and Ricci Curvature overApril-July, 2008. As part of this French activity in arapidly-developing area of geometric analysis, an InternationalConference on Ricci Flow is scheduled for June 30-July 4, 2008 asa conclusion to the trimester. Topics of the trimester andconference are expected to include Ricci flow in thegeometrization of three-manifolds, Kaehler-Einstein metrics andKaehler-Ricci flow, metrics of constant scalar curvature, Ricciflow in dimensions four and higher, analytic aspects of geometricflows, Einstein metrics and recent developments in geometricrelativity, synthetic Ricci curvature, and Ricci limit spaces.This landscape was transformed by Perelman's work on Ricci flowin three-manifolds and all of these areas have enjoyed recentadvances.This award provides partial support for expenses of US-basedparticipants in the Paris conference, particularly graduatestudents and junior researchers. The subject of the workshop isthe Ricci flow and its extensions. This differential equationand technique in geometry became celebrated with its applicationby Perelman and Hamilton to the Poincare Conjecture on thetopological uniqueness of the three-dimensional sphere, one ofthe great challenge problems of mathematics. The techniqueconsiders a single space with a large number of metrics (ways tomeasure distance in the space) by using the Ricci curvature ateach metric to determine a direction for evolving the metric thatis likely to make the metric more symmetric -- loosely speaking,we try to change in the direction of ever rounder metrics.Although it is often difficult to control all the detailsnecessary to make such an argument succeed, geometers have foundthat this idea identifies optimal metrics in a variety ofimportant situations. The conference web page ishttp://www.ihp.jussieu.fr/ceb/Trimestres/T08-2/C2/index.html.