On Irreducibility of the Bloch Variety

Abstract: Given a ZZ^2 periodic graph G, the Schrodinger operator associated to G is a graph Laplacian with a potential. After a Fourier transform we can represent our operator as a finite matrix whose entries are Laurent polynomials. The vanishing set of this characteristic polynomial is the Bloch variety. Questions regarding the algebraic properties of this object are of interest in mathematical physics. We will focus our attention on the irreducibility of this variety. Understanding the irreducibility of the Bloch variety is important in the study of the spectrum of periodic operators, providing insight into quantum ergodicity. In this talk we will present results on preserving irreducibility of the Bloch variety after changing the period lattice. This is joint work with Jordy Lopez.

computational geometrydiscrete mathematicscommutative algebracombinatorics

Audience: researchers in the topic

Copenhagen-Jerusalem Combinatorics Seminar

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