Florio M. Ciaglia (Max-Planck-Institut, Leipzig)
Friday 13th of December 2019, 15:30, ICMAT, Aula Naranja
Monday 2nd of December 2019, 15:30, UC3M, Seminar Room 2.2D08
Olaf Post (Universität Trier)
Spectral gaps, discrete magnetic Laplacians and spectral ordering
Friday 15th of November 2019, 12:30, ICMAT, Aula Gris 1
In this talk, we localise the spectrum of a discrete magnetic Laplacian on a finite graph using techniques similar to the Dirichlet-Neumann-bracketing for continuous problems. As application we localise the spectrum of periodic Laplacians using the fact that the fibre operators from Floquet Bloch theory can be seen as magnetic Laplacians. Finally, we use the bracketing ideas to order spectra of different graphs, and show how certain graph manipulations change the spectrum.
David Krejcirik (Czech Technical University, Prague).
Spectral geometry of quantum waveguides
Friday 13th of September 2019, 15:00, ICMAT, Aula Naranja
We shall make an overview of the interplay between the geometry of tubular neighbourhoods of Riemannian manifold and the spectrum of the associated Dirichlet Laplacian. An emphasis will be put on the existence of curvature-induced eigenvalues in bent tubes and Hardy-type inequalities in twisted tubes of non-circular cross-section. Consequences of the results for physical systems modelled by the Schroedinger or heat equations will be discussed.