14 jul 2020

WADE Lisbon (5pm)

password: ask the organizers

Abstract.

The talk focuses on the influence of the vertex coupling on spectral properties of periodic quantum graphs. Specifically, two questions will be addressed. The first concerns the number of open spectral gaps; it is shown that graphs with a nontrivial coupling can have finite but nonzero number of them. Secondly, motivated by recent attempts to model the anomalous Hall effect, we investigate a class of vertex couplings that violate the time reversal invariance. For the simplest coupling of this type we show that its high-energy properties depend on the parity of the lattice vertices, and discuss various consequences of this property.

• webinar in Nonlinear analysis and differential equations