Abstract: Models of aperiodic order and quasicrystals tend to exhibit very delicate spectral properties, such as Cantor spectrum and fractal spectral dimension. We discuss algorithms for computing spectral quantities associated with models of aperiodic order. The algorithms are optimal with respect the solvability computability index (SCI), which can be shown by synthesizing tools from SCI and the general theory of ergodic Schrödinger operators.

Contact: Giorgio Young