Quolloquium: Spectral geometry of quantum waveguides

Other Talks
Wednesday, September 20, 2017 - 1:00pm for 1 hour (actually 50 minutes)
Skiles 255
David Krejcirik – Czech Technical University – krejcirik@ujf.cas.czhttp://gemma.ujf.cas.cz/~krejcirik/
Evans Harrell

Please Note: NOTE: This is the first in a forthcoming series of colloquia in quantum mathematical physics that will take place this semester. The series is a spin-off of last year's QMath conference, and is intended to be of broad interest to people wanting to know the state of the art of current topics in mathematical physics.

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.