Search

Workshop

Irreducibility of the Dispersion Polynomial for Periodic Graphs

  • Matthew Faust (Texas A&M University, USA)
E1 05 (Leibniz-Saal)

Abstract

Given a ZZ^d-periodic graph G, a periodic potential together with a weighted graph Laplacian defines a discrete periodic operator, which acts on functions on the vertices of G. Floquet theory allows us to study the spectrum of this operator through a finite matrix with Laurent polynomial entries. The zero set of the corresponding characteristic polynomial is called the Bloch variety. We will focus on the reducibility of this variety, which provides insights into various spectral properties, such as quantum ergodicity. In particular, we will study how the reducibility of the Bloch variety is affected as one varies the period of the potential.

conference
29.07.24 02.08.24

MEGA 2024

MPI für Mathematik in den Naturwissenschaften Leipzig (Leipzig) E1 05 (Leibniz-Saal)
Universität Leipzig (Leipzig) Felix-Klein-Hörsaal

Mirke Olschewski

Max Planck Institute for Mathematics in the Sciences Contact via Mail

Saskia Gutzschebauch

Max Planck Institute for Mathematics in the Sciences Contact via Mail

Christian Lehn

Ruhr-Universität Bochum

Irem Portakal

Max Planck Institute for Mathematics in the Sciences

Rainer Sinn

Universität Leipzig

Bernd Sturmfels

Max Planck Institute for Mathematics in the Sciences

Simon Telen

Max Planck Institute for Mathematics in the Sciences

Upcoming Events of this Conference