15th New Mexico Analysis Seminar
February 19-21, 2016
University of New Mexico
Albuquerque, New Mexico, USA

Mini Course

Christopher Sogge

J.J. Sylvester Professor
Johns Hopkins University

Global Harmonic Analysis and the Concentration of Eigenfunctions

Abstract: We shall go over several problems related to the concentration of eigenfunctions. The study of eigenfunction concentration naturally arises in analysis, number theory and mathematical physics. The tools that we use to analyze these problems are based on microlocal and harmonic analysis, as well as Riemannian geometry. More specifically, we shall show how classical results from the propagation of singularities, bilinear oscillatory integral estimates and the Cartan-Hadamard theorem as well as comparison theorems from geometry play a natural role in the analysis of this phenomena. We shall show that, even though extreme concentration occurs on manifolds of positive curvature, it cannot occur on manifolds of negative curvature.

The conference is sponsored by
National Science Foundation
Grant DMS-1400429

Simons Foundation and Efroymson Foundation

We intend to pay for shared accommodations for participants who request support, and if there are funds left, reimburse some travel expenses (priority given to speakers, junior participants, females, and minorities).

Please register by Tuesday, January 19 to be considered for hotel accommodations and partial travel support.