Conference on Quadrature Domains and Related Topics; March 27-30, 2003, Santa Barbara, California

30年前，D.Aharonov和h.s.s hapiro提出了满足所有可积调和函数的精确高斯正交的平面域，这些具有真实代数边界的刚性集成为保形映射、流体力学、近似理论、势理论、图像处理和算子理论等各种问题的重要研究对象。这些领域的顶尖专家将出席会议，并讨论这一广泛领域的未来研究方向。会议将专门讨论一类平面形状，称为正交域，它是由间接测量有限确定的。事实证明，它们对于从地球物理学逆问题、流体流动到层析成像等应用都很重要。会议将为年轻的研究人员提供一个独特的机会，与所有相关领域的专家会面，并分享有关正交领域的想法和信息。

The class of planar domains which satisfy an exact Gaussian quadrature for all integrable harmonic functionswas introduced 30 years ago by D.Aharonov and H.S.Shapiro.These rather rigid sets, with real alegbraic boundary,turned out to be essential objects of investigation in avariety of problems related to conformal mapping, fluidmechanics, approximation theory, potential theory, imageprocessing and operator theory. Top experts in these areaswill attend the conference and will discuss the futuredirections of research in this broad area.The conference will be devoted to a class of planar shapes,called quadrature domains, which are finitely determined byindirect measurements. They turn out to be important forapplications ranging from inverse problems of geophysicsand fluid flows to tomography. The meeting will be a uniqueopportunity for young researchers to meet experts in alladjacent areas and to share ideas and information aboutquadrature domains.