## AMUSE

**Date:** November 11, 2019

**Time:** 6:00PM - 7:00PM

**Location:** BLOC 220

**Speaker:** Gregory Berkolaiko, Dept of Mathematics, Texas A&M University

**Title:** *Diabolical points and where to find them*

**Abstract:** Wave propagation through periodic medium (such as a crystal or a layered material) is described by dispersion relation, which in most practical computations is a plot of eigenvalues of a matrix which depends on several parameters. Gaps in the dispersion relation correspond to wave frequencies that do not propagate through the material. Diabolical points refer to a special feature in the dispersion relation, a location where two eigenvalues collide. Those are special because a small perturbation of the medium (for example, by a external magnetic field) can create a new gap and thereby turn a conductor into an insulator. We describe the idea behind a numerical algorithm we designed to locate diabolical points for a parametric family of real symmetric matrices. Based on an undergraduate research project of Advait Parulekar.