A Conference on Harmonic Analysis at the University of Iceland

冰岛大学谐波分析会议

• 批准号: 0653817
• 负责人: David Vogan
• 金额: $ 5万
• 依托单位: Massachusetts Institute of Technology
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-07-01 至 2008-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0653817&HistoricalAwards=false
• 关键词: Conference; Harmonic; Analysis; University; Iceland

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.

2007年8月15-18日，冰岛大学将举行一次关于齐次空间和李群的会议。这次会议的目的是让对这一领域感兴趣的数学家们以许多不同的方式聚集在一起，了解最近的工作和仍然存在的未决问题。基本问题本质上是解析的：例如，理解群不变微分算符的谱，或者Radon变换的反演公式。然而，在这些问题上的进展通常涉及到数学的其他部分的复杂工具：Harish-Chandra创建的半单群上球函数的渐近展开与李代数的Verma模之间的关系；广义Verma模的零化子与Radon变换的像之间的关系；或者将对称空间上的特征函数与主级数表示联系起来的Helason猜想。在每一种情况下，以及在更多类似的情况下，调和分析问题、群论问题和代数问题之间都存在着深刻的、意想不到的联系。因此，如果不理解其他主题，这些主题中的任何一个都没有意义。不幸的是，数学的专门化会让人们更难看到这些联系。表示理论是为调和分析而创建的；然而，学生和年轻的数学家经常将其作为一门纯粹的代数学科来学习，并且错过了分析中的根所能提供的意义和力量。同样，研究函数空间和微分方程式的人可能不知道可用的代数工具。这次在冰岛大学举行的会议为年轻人提供了一个独特的机会，让他们全面了解均匀空间的调和分析。该奖项将为来自美国的最多12名受邀参与者以及大约12名来自美国的受邀参与者提供旅费和住宿费。受邀参与者是由组委会挑选的。对于另外12名参与者，我们将向研究生征集申请。