Colloquium; Douglas N. Arnold (University of Minnesota) : Computing spectra without solving eigenvalue problems

Abstract: The puzzling and important phenonenon of wave localization arises in many physical and mathematical contexts, with applications ranging from the quantum mechanics of electrical conduction to the construction of noise abatement systems, to name but a few. Although studied by physicists and mathematicians for the better part of a century, localization of eigenmodes is still not fully understood nor controlled. 

In this talk we will describe recent major strides which have been made towards a comprehensive theory. In particular, it is now possible to predict the spectrum --both the eigenfunctions and the eigenvalues-- of a large class of elliptic PDE, particularly Schr√∂dinger operators with random potentials. The talk will feature numerous high fidelity large scale finite element computations which have played a crucial role in guiding our understanding, validating theoretical results, and highlighting mysteries as yet unexplained.

Coffee/tea and cookies will be served from 12.15 to 12.45.

Published Apr. 28, 2017 1:44 PM - Last modified May 2, 2017 2:11 PM