Topological stability from spectral analysis

The aim is to use mathematical scattering theory to find and study new topological features of the spectra of lineartransformations on Hilbert space. The significance derives from mathematical models of low temperatureconducting quantum materials. These have revealed topological phases of matter' that are stable with respect toa range of variations in the parameters that determine the system. The stability is desired for applications toquantum devices. Our results will give topological stability from the scattering spectrum, a feature not previouslyseen. The benefits stem from new results in mathematical scattering theory with a primary novelty being theanalysis of zero energy resonances in mathematical models of graphene.