Great Lakes Geometry Conference

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AbstractAward: DMS-0302452Principal Investigator: Xiu Xiong ChenThe next Great Lakes Geometry Conference will be held May 1 - 4,2003 at the University of Wisconsin-Madison. This is aninternational conference held annually in the Midwest region,rotating among different universities. The aim of this conferencewill be to introduce the latest developments in the field ofgeometric analysis and some closely related areas. A partiallist of topics which will be covered by this conference include:(Kaehler-) Einstein equation and constant scalar curvature metricequation (Yamabe problem); (Hermitian-) Yang-Mills equation;minimal surface equation; harmonic map problem and J- holomorphiccurves (Cauchy-Riemann equation); and the geodesic equation inthe infinite dimensional space of Kaehler metrics which is givenby a homogenous complex Monge-Ampere equation. These equationsfit together with the corresponding evolution equations:(Kaehler-) Ricci flow, Yang-Mills flow, the mean curvature flow,and the harmonic map flow, etc. People would like to know (localand global) existence, regularity and uniqueness of solutions tothese equations. Many deep works have arisen by studyingdifferent aspects of these challenging problems.Differential geometry is a fundamental and vital field ofmathematics which has many far reaching applications beyond therealm of pure mathematics. To name a few: the study of Kaehlergeometry, especially Calabi-Yau manifolds, has importantapplications in theoretical physics; the study of (inverse) meancurvature flow has important applications in image processing;and the study of curves, surfaces and their higher-dimensionalanalogues have important applications in computer graphics,engineering and optimization.