A Conference on Harmonic Analysis at the University of Iceland

Massachusetts Institute Of Technology, Cambridge MA

Investigators

Abstract

Abstract Vogan On 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.