Algebra and Combinatorics Seminar

Date: April 19, 2024

Time: 3:00PM - 4:00PM

Location: BLOC 302

Speaker: Matthew Faust, TAMU

Title: Irreducibility of the Bloch Variety

Abstract: Given a ZZ^d-periodic graph G, a discrete periodic operator, a periodic potential together with a weighted graph laplacian, acts on functions on the vertices of G. Floquet theory allows us to study the spectrum through a finite matrix with Laurent polynomials entries. The zero set of the corresponding characteristic polynomial is called the Bloch variety. We will focus our attention on the irreducibility of this variety, which provides insight into quantum ergodicity. In particular we study how irreducibility of the Bloch variety is affected as one varies the period of the potential.