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

里奇流国际会议，法国巴黎，2008 年 6 月 30 日至 7 月 4 日

• 批准号: 0704193
• 负责人: John Lott
• 金额: $ 5.15万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-06-01 至 2009-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0704193&HistoricalAwards=false
• 关键词: International; Conference; Ricci; Flow; Paris

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.

摘要奖：DMS-0704193 主要研究者：John W.位于巴黎的亨利·庞加莱研究所（IHP）将于2008年4月至7月举办一个为期四个月的关于里奇流和里奇曲率的项目。 作为法国在快速发展的几何分析领域活动的一部分，一个关于里奇流的国际会议定于2008年6月30日至7月4日举行阿萨三个月的结束。 三个月和会议的主题预计将包括三维流形的几何化中的里奇流，Kaehler-Einstein度量和Kaehler-Ricci流，常数标量曲率的度量，四维和更高维的里奇流，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，合成里奇曲率，和Ricci极限空间。这一景观是由佩雷尔曼的工作改变了Ricci流在三个流形和所有这些领域都享有最近的进步。这个奖项提供了部分支持的费用，美国-基于巴黎会议的参与者，特别是研究生和初级研究人员。 研讨会的主题是Ricci流及其扩展。 这个微分方程和技术在几何成为著名的应用程序佩雷尔曼和汉密尔顿的庞加莱猜想的拓扑唯一性的三维领域，一个伟大的挑战性问题的数学。 该技术考虑了具有大量度量的单个空间（测量空间距离的方法）通过使用每个度量的Ricci曲率来确定度量的发展方向，这可能使度量更对称--粗略地说，我们试图改变更圆的度量的方向。尽管通常很难控制使这样的论证成功所需的所有细节，几何学家们已经发现，这种思想在各种重要的情况下确定了最佳的度量。 会议网页：http：www.ihp.jussieu.fr/ceb/Trimestres/T08-2/C2/index.html。