Speaker: Pavel Exner (Doppler Institute for Mathematical Physics and Applied Mathematics, Prague).

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.

To get access to the password, please register on the website or contact one of the organizers.

The Lisbon Webinar in Analysis in Differential Equations is a joint iniciative of CAMGSD, CMAFcIO and GFM, three research centers of the University of Lisbon. It is aimed at filling the absence of face-to-face seminars and wishes to be a meeting point of mathematicians working in the field.