Spectral Structures and Topological Methods in Mathematical Quasicrystals

Topological States and adiabatic pumping in quasicrystals.

The unrelated discoveries of quasicrystals and topological insulators have in turn challenged prevailing paradigms in condensed-matter physics. We find a surprising connection between quasicrystals and topological phases of matter: (i) quasicrystals exhibit nontrivial topological properties and (ii) these properties are attributed to dimensions higher than that of the quasicrystal. Specifically...

Classical mathematical structures within topological graph theory

Finite simple graphs are a playground for classical areas of mathematics. We illustrate this by looking at some results.

A Guide to Mathematical Quasicrystals

Quasicrystals and Other Aperiodic Structures in Mineralogy

In this article, we first present and discuss eighteenth-century descriptions of minerals that contributed decisively to the development of crystallography. Remarkably, these old crystallographic descriptions included morphologies with symmetries incompatible with an internal periodic order of atoms, which, however, have been recognised to be characteristics of quasicrystals. Moreover, we also ...

Mathematical methods for spectral image reconstruction

We present a method for recovery of damaged parts of old paintings (frescoes), caused by degradation of the pigments contained in the paint layer. The original visible colour information in the damaged parts can be faithfully recovered from measurements of absorption spectra in the invisible region (IR and UV) and from the full spectral data of the well preserved parts of the image. We use the ...