Abstract

I will give an overview of my work over the last 15 years, with collaborators including Marko Lindner (TU Hamburg), Ratchanikorn Chonchaiya (King Mongkut’s University of Technology, Bangkok), Raffael Hagger (Kiel), and Brian Davies (KCL), on computing the spectra and pseudospectra of banded and band-dominated operators. This will include describing algorithms that, given appropriate inputs, can produce a convergent sequence of approximations to the spectrum of an arbitrary band-dominated operator, with the property that each member of the sequence can be computed in finitely many arithmetical operations. We give a concrete implementation of the algorithm for operators that are pseudoergodic in the sense of Davies (Commun. Math. Phys. 2001) and illustrate this algorithm by spectral computations for the beautiful Feinberg-Zee random hopping matrix. Details can be found at https://arxiv.org/abs/2401.03984