AMUSE

Date: October 7, 2015

Time: 6:20PM - 6:35PM

Location: BLOC 113

Speaker: Madeline Hansalik, Texas A&M University, Department of Mathematics

Title: Magnetic Spectral Decimation on the Diamond Fractal

Abstract: The Laplacians for a large class of self-similar fractals and fractal graphs exhibit a property called spectral decimation, in which the spectra of different levels of approximation are related by a dynamical system involving a rational function. Expanding upon the work of Malozemov and Teplyaev, we extend some aspects of the spectral decimation method from the Laplacian operator to a magnetic Laplacian operator, and use this to numerically investigate properties of the magnetic spectrum of this operator on the diamond fractal. In particular, we identify the correct unitary transformations and projections to obtain the aforementioned rational functions.