On Monday at 3:30 PM in Math 357, Dr. Tracy Weyand of Baylor University will be talking about “The Spectra of the Magnetic Schrodinger Operator on Graphs.

Abstract: In the most general sense, a graph represents a relationship between a set of objects. Applications appear in chemistry, physics, engineering, computer science, and social science to name a few. In most applications, the relationship between objects (vertices) is represented by an operator that acts on functions whose domain is the graph. My research focuses on studying the spectra and corresponding eigenfunctions of such operators.

Throughout this talk, we will consider two types of graphs: discrete and metric. Eigenvalues of the magnetic Schrodinger operator on both types of graphs can be considered functions of the magnetic flux on the graph. Viewing the eigenvalues as functions, we have been able to determine their Morse index (a measure of stability). This result has led to progress on several other problems including the inverse problem (information the eigenvalues provide about the structure of a graph) and the location of Dirac cones (touching points) in the spectral bands (as well as properties of the corresponding eigenfunctions there).