Mathematical Physics and Harmonic Analysis Seminar

Date: April 16, 2021

Time: 2:00PM - 3:00PM

Location: Zoom

Speaker: Cosmas Kravaris, Texas A&M University

Title: On the density of eigenvalues on discrete periodic graphs

Abstract: Using the Floquet-Bloch transform, we show that Zd-periodic graphs have finitely many finite support eigenfunctions up to translations and linear combinations and show that this can be used to calculate the density of eigenvalues. We study the Kagome lattice to illustrate these techniques and generalize the claims to amenable quasi-homogeneous graphs whose acting group has Noetherian group algebra (this includes all virtually polycyclic groups). Finally, we provide a formula for the von Neumann dimension (i.e. density) of eigenvalues on Zd-periodic graphs using syzygy modules.