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

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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.