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

摘要：项目负责人：John W. lott巴黎庞加莱研究所（IHP）将于2008年4 - 7月举办为期3个月的里奇流和里奇曲率研究项目。作为法国在快速发展的几何分析领域的活动的一部分，将于2008年6月30日至7月4日召开一次关于利玛奇流的国际会议，作为三个月的总结。本学期和会议的主题预计将包括三流形几何化中的Ricci流、Kaehler-Einstein度量和kaehler -Ricci流、常数标量曲率的度量、四维及更高维度的Ricci流、几何流的解析方面、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。佩雷尔曼关于三流形利玛窦流的研究改变了这一景观，所有这些领域最近都取得了进展。该奖项为巴黎会议的美国参与者，特别是研究生和初级研究人员提供部分费用支持。研讨会的主题是利玛窦流及其延伸。由于佩雷尔曼和汉密尔顿将这种微分方程和技术应用于庞加莱关于三维球面拓扑唯一性的猜想，这是数学的重大挑战问题之一，因此在几何学中变得著名。该技术考虑具有大量度量（在空间中测量距离的方法）的单个空间，通过使用每个度量的里奇曲率来确定度量的发展方向，这可能使度量更加对称——宽泛地说，我们试图在更圆的度量的方向上改变。虽然通常很难控制所有必要的细节，使这样的论点成功，几何学家已经发现，这个想法确定了各种重要情况下的最佳度量。会议网页https://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.