Mathematical Physics and Harmonic Analysis Seminar

Date: October 29, 2021

Time: 1:50PM - 2:40PM

Location: Zoom

Speaker: Burak Hatinoglu, UC Santa Cruz

Title: Spectral properties of the periodic 4th order Schrodinger operator on the hexagonal lattice

Abstract: This talk will focus on the 4th order Schr\"{o}dinger operator $d^4/dx^4 + q(x)$ on the hexagonal lattice (graphene) and its geometric perturbations with self-adjoint vertex conditions and a real periodic symmetric potential $q$. I will consider the following spectral properties of this Hamiltonian on graphene: absolutely continuous, singular continuous and pure-point spectra, dispersion relation, singular Dirac points and energy levels of reducible Fermi surfaces. I will also discuss some of these spectral properties for the same operator on lattices in the geometric neighborhood of graphene. This talk is based on a joint work with Mahmood Ettehad (University of Minnesota).