A Conference on Harmonic Analysis at the University of Iceland

2007年8月15日至18日，冰岛大学将举行一个关于齐次空间和李群的会议。 会议的目的是汇集数学家的利益，在这一领域出现在许多非常不同的方式，了解最近的工作和开放的问题仍然存在。基本问题是分析性质的：例如，理解群不变微分算子的谱，或Radon变换的反演公式。然而，这些问题的进展往往涉及复杂的工具，从其他部分的数学：之间的关系创建的哈里什-钱德拉渐近展开球面函数的半单群和Verma模块的李代数;零化子之间的关系广义Verma模块和图像的拉东变换;或赫尔加松的猜想有关本征函数的对称空间的主要系列表示。在每一种情况下，以及在许多类似的情况下，调和分析、群论和代数问题之间都有着深刻而意想不到的联系。因此，如果不理解其他学科，这些学科都没有意义。 不幸的是，数学专业化会使这些联系更难被发现。表示论是为调和分析而创立的;然而，学生和年轻的数学家们常常把它当作一门纯粹的代数学科来学习，而忽略了根在分析中所能提供的意义和力量。同样，学习函数空间和微分方程的人可能不知道可用的代数工具。 在冰岛大学举行的这次会议为年轻人提供了一个独特的机会，让他们能够更广泛地了解均匀空间上的谐波分析。该奖项将为来自美国的12名受邀与会者以及来自美国的12名与会者提供旅行和住宿资金。受邀与会者由组委会挑选。对于额外的12名参与者，我们将寻求研究生的申请。

AbstractVoganOn August 15-18, 2007, there will be a conference at the University of Iceland on homogeneous spaces and Lie groups. The purpose of the conference is to bring together mathematicians whose interests in this field arise in many very different ways, to learn about recent work and about open problems that remain. The fundamental questions are analytic in nature: understanding the spectra of group-invariant differential operators, for example, or inversion formulas for Radon transforms. Yet progress on these questions has often involved sophisticated tools from other parts of mathematics: the relationship created by Harish-Chandra between asymptotic expansions of spherical functions on semisimple groups and Verma modules for the Lie algebra; the relationship between annihilators of generalized Verma modules and the image of the Radon transform; or Helgason's conjecture relating eigenfunctions on symmetric spaces to principal series representations. In each of these cases, and in many more like them, there are deep and unexpected connections between questions of harmonic analysis, of group theory, and of algebra. As a result, none of these subjects makes sense without an understanding of the others. Unfortunately, mathematical specialization can make these connections harder to see. Representation theory was created for harmonic analysis; yet students and young mathematicians often learn it as a purely algebraic subject, and miss both the meaning and the power that the roots in analysis can provide. In the same way, individuals studying function spaces and differential equations may be unaware of algebraic tools that are available. The conference at the University of Iceland provides a unique opportunity for young people to get a broad picture of harmonic analysis on homogeneous spaces.This award will provide funding for travel and lodging for up to twelve invited participants from the US, and for about twelve more participants from the US.The invited participants were chosen by the organizing committee. For the twelve additional participants, we will seek applications from graduate students.