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Great Lakes Geometry Conference

Abstract<br/><br/>Award: DMS-0302452<br/>Principal Investigator: Xiu Xiong Chen<br/><br/>The next Great Lakes Geometry Conference will be held May 1 - 4,<br/>2003 at the University of Wisconsin-Madison. This is an<br/>international conference held annually in the Midwest region,<br/>rotating among different universities. The aim of this conference<br/>will be to introduce the latest developments in the field of<br/>geometric analysis and some closely related areas. A partial<br/>list of topics which will be covered by this conference include:<br/>(Kaehler-) Einstein equation and constant scalar curvature metric<br/>equation (Yamabe problem); (Hermitian-) Yang-Mills equation;<br/>minimal surface equation; harmonic map problem and J- holomorphic<br/>curves (Cauchy-Riemann equation); and the geodesic equation in<br/>the infinite dimensional space of Kaehler metrics which is given<br/>by a homogenous complex Monge-Ampere equation. These equations<br/>fit together with the corresponding evolution equations:<br/>(Kaehler-) Ricci flow, Yang-Mills flow, the mean curvature flow,<br/>and the harmonic map flow, etc. People would like to know (local<br/>and global) existence, regularity and uniqueness of solutions to<br/>these equations. Many deep works have arisen by studying<br/>different aspects of these challenging problems.<br/><br/>Differential geometry is a fundamental and vital field of<br/>mathematics which has many far reaching applications beyond the<br/>realm of pure mathematics. To name a few: the study of Kaehler<br/>geometry, especially Calabi-Yau manifolds, has important<br/>applications in theoretical physics; the study of (inverse) mean<br/>curvature flow has important applications in image processing;<br/>and the study of curves, surfaces and their higher-dimensional<br/>analogues have important applications in computer graphics,<br/>engineering and optimization.

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