Skip to content
Texas A&M University
Mathematics

Geometry Seminar

Date: April 30, 2021

Time: 4:00PM - 5:00PM

Location: Zoom

Speaker: Matthew Faust, Texas A&M University

  

Title: The number of critical points of dIscrete periodic operators

Abstract: The spectral gap conjecture is a well known and widely believed conjecture in mathematical physics concerning the structure of the Bloch variety (dispersion relation) of periodic operators. The Bloch variety of a discrete operator is algebraic, inviting methods from algebraic geometry to their study.

Motivated by this this conjecture, this talk will introduce a bound on the number of critical points of the dispersion relation for discrete periodic operators, and provide a general criterion for when this bound is achieved. We also present classes of periodic graphs for when this criteria is satisfied for Laplace-Beltrami operators. This is joint work with Frank Sottile.