Differential Operators on Graphs and Waveguides

February 25 -- March 1, 2019 | TU Graz, Austria

Slides of the talks

Monday talks

Anne-Sophie Bonnet-Ben Dhia   A new complex frequency spectrum for the analysis of transmission efficiency in waveguide-like geometries
Pavel Exner Spectra of periodic quantum graphs: more than one would expect
Philippe Briet Absence of the singular spectrum in a twisted Dirichlet-Neumann waveguide
Luka Grubisic Constrained evolution problems on a metric graph
Harald Woracek On a problem of Louis de Branges (blackboard lecture)
Anton Kutsenko Application of matrix-valued integral continued fractions to spectral problems on periodic graphs with defects
Julien Royer Local energy decay for the wave equation in a dissipative waveguide
Anna Muranova On the notion of effective impedance via ordered fields
Michal Jex Trace Hardy inequality for Euclidean space with cut
Raphael Pruckner Estimate for the Weyl coefficient of a two-dimensional canonical system (blackboard lecture)

Tuesday talks

Christiane Tretter Spectral problems on star graphs
Pavel Kurasov Quantum graphs and almost periodic functions
Wolfgang Woess Boundary representations of lambda-harmonic and polyharmonic functions on trees
Jon Harrison Quantum graph properties via pseudo orbits and Lyndon words
Oleg Sarafanov Asymptotic and numerical study of resonant tunneling in a 2D quantum waveguide with several resonators
Diana Barseghyan Spectral geometry in a rotating frame: properties of the ground state
Vladimir Lotoreichik Spectral gap for graphene quantum dots
Noema Nicolussi Quantum graphs on radially symmetric antitrees
Joachim Kerner Spectral theory of an interacting two-particle system on the half-line
Andrea Serio Optimal potentials on quantum graphs with delta-couplings

Wednesday talks

Aleksey Kostenko Infinite quantum graphs
Michael Plum TM-mode spectrum created by waveguides in photonic bandgap structures
Ian Wood Weak localization results for TE-modes
Jonathan Rohleder Hot spots of quantum graphs
Daniela Maier Breather solutions on periodic necklace graphs
Simon Becker Periodic quantum graphs in homogeneous magnetic fields
Jiri Lipovsky A Gelfand-Levitan trace formula for generic quantum graphs

Thursday talks

Delio Mugnolo Spectral partitions of quantum graphs
Konstantin Pankrashkin Robin eigenvalues on domains with peaks (blackboard lecture)
Natalia Saburova Schrödinger operators with guided potentials on periodic graphs
Igor Popov Weyl asymptotics of resonances and resonance states completeness for quantum graphs
Giuseppe Cardone Norm-resolvent convergence for elliptic operators in a planar waveguide perforated along a curve
Kamila Debowska Direct and inverse problems for one-dimensional Dirac operators with nonlocal potentials
Selim Sukhtaiev Localization for Anderson models on tree graphs
Marvin Plümer An eigenvalue bound for the Kirchhoff-Laplacian on planar quantum graphs
Jan Simmer Approximation of the Laplacian on the Sierpinski Gasket: norm resolvent and spectral convergence
Valentina Franceschi Point interactions for 3D sub-Laplacians

Friday talks

David Krejcirik Waveguides with asymptotically diverging twisting
Olaf Post Perturbations of manifolds and spectral convergence
Biaggio Cassano Self-adjointness and spectral properties for the Dirac operator with Coulomb-type perturbations
Markus Holzmann The Landau Hamiltonian coupled with an electric delta-potential