Mathematical Physics and Harmonic Analysis Seminar

Date: March 11, 2022

Time: 1:50PM - 2:50PM

Location: BLOC 302

Speaker: Matthew Faust, TAMU

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 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 a class of periodic graphs for when this criteria is satisfied for Laplace-Beltrami operators. This is joint work with Frank Sottile.