Posted August 21, 20203:10 pm - 4:00 pm Zoom
C. Douglas Haessig, University of Rochester
Posted August 22, 2020
Last modified September 14, 2020
Stephen Shipman, Mathematics Department, LSU
Introduction to Fourier analysis for Z^d and applications
The aim of my talks is to develop the Fourier analysis underlying the study of periodic operators; to show how the theory is applied to phenomena of crystal-type structures in solid-state physics; and to indicate the kinds of problems of interest today. The first talk will concentrate on the Fourier analysis for actions of Z^d and its finite-index extensions. The second talk will delve into aspects of the spectrum of periodic operators and their perturbations, including continuous pre-fractal and fractal continuous spectrum; and eigenvalues embedded in the continuum. The third talk will continue with topics of current interest, such as Dirac cones in graphene, multi-layer structures, Berry phase, twisted bi-layer graphene, etc.