Conference on Geometric Analysis: Present and Future; Cambridge, MA, August 2008

AbstractAward：DMS-0706214首席研究员：季丽珍该奖项为2008年夏末在马萨诸塞州剑桥举行的为期六天的几何分析及相关领域会议提供部分支持。 这次会议的目的是全面概述几何分析的现状和未来发展方向，以及它与代数几何、分析、拓扑学、数学物理和弦理论等许多领域的联系。这次关于几何分析和相关几何学科的大型会议的召开正值该领域领导人之一丘成桐的六十岁生日。 几何分析是一系列几何问题和思想的集合，通常涉及大尺度上几何空间的性质，分析技术开始于小尺度的几何特征，有时允许我们将其外推到大尺度的陈述。 几何分析的两个伟大成就是卡拉比猜想（Calabi Conjecture）和庞加莱猜想（Poincare Conjecture），前者是丘尔森在20世纪70年代解决的，后来被发现是弦理论发展的关键，后者是一个悬而未决了100多年的著名问题，直到几年前才被G.佩雷尔曼使R.汉密尔顿。 许多结果和technologesdeveloped在过去的三十年中，在几何分析和微分几何是必不可少的证明庞加莱猜想，和思想贡献的问题Perelman掀起了世界范围内的活动新的问题在geometricanalysis。 欲了解更多信息，请访问会议网站http：pamq.henu.edu.cn/add/Yau/index.html。

AbstractAward: DMS-0706214Principal Investigator: Lizhen JiThis award provides partial support for six days of meetings inCambridge, Massachusetts during late summer 2008 on geometricanalysis and related fields. The conference aims to develop acomprehensive overview of the present status and futuredirections of geometric analysis and its connections to manyareas including algebraic geometry, analysis, topology,mathematical physics, and string theory.The occasion for this large conference on geometric analysis andrelated geometric subjects is the sixtieth birthday of Shing-TungYau, one of the leaders in the area. Geometric analysis is amarriage of geometric problems and ideas, which often concernproperties of geometric spaces on large scales, with analytictechniques that begin with small-scale features of geometry andsometimes allow us to extrapolate those to large-scalestatements. Two of the great successes of geometric analysis arethe Calabi Conjecture, settled by Yau in the 1970s and laterfound to be a key to the development of string theory, and thePoincare Conjecture, a celebrated problem that was open for morethan one hundred years before its resolution just a few years agoby G. Perelman, who brought to maturity a program launched in the1980s by R. Hamilton. Many of the results and techniquesdeveloped over the last thirty years in geometric analysis anddifferential geometry were essential to the proof of the PoincareConjecture, and the ideas contributed to the problem by Perelmanhave set off worldwide activity on new questions in geometricanalysis. For more information see the conference web site,http://pamq.henu.edu.cn/add/Yau/index.html.