Seminar

In this talk, I study a PDE that models interface effects between insulators. It is a Schrodinger equation with periodic asymptotics (the bulk), away from a strip (the interface). I will prove the bulk-edge correspondence. At the physical level, this index-like theorem predicts that the interface between two topologically distinct insulators behaves like a conductor.  

The proof relies on a semiclassical trace expansion, though the original problem is not semiclassical. It suggests that energy propagates along the interface in the form of waves  microlocalized at the singularities of an underlying (Bloch) bundle. This draws an apparently new connection between microlocal analysis and condensed matter physics.