Mathematisches Kolloquium

Zusammenfassung: Hamiltonian operators describing periodic quantum systems subject to constant magnetic fields give rise to interesting spectral and geometric structures. For the simplest possible model the fractal nature of the spectrum is nicely depicted in the famous Hofstadter butterfly and analyzed in the work of last year's fields medalist A. Avila. In my talk I describe recent results on an approximate block decomposition, called Peierls substitution in physics, of perturbations of such Hamiltonians. For this problem also the underlying geometric structure given by certain complex vector bundles over the torus becomes relevant. As I will explain, a key technical ingredient for our analysis is then a geometric calculus for pseudodifferential operators acting on sections of such vector bundles. This is based on joint work with Silvia Freund.

Alle Interessierten sind hiermit herzlich eingeladen. Eine halbe Stunde vor dem Vortrag gibt es Kaffee und Tee im Sozialraum (Raum 448) im 4. Stock.

Treffpunkt zum Abendessen um 18.00 Uhr wird noch bekannt gegeben.