Mathematical Physics and Harmonic Analysis Seminar

Date: August 30, 2019

Time: 1:50PM - 2:50PM

Location: BLOC 628

Speaker: P. Kuchment

Title: CANCELLED

Abstract: due to the funeral of Professor Michael Boshernitzan (Rice U.)

Analyticity of the spectrum and Dirichlet-to-Neumann operator technique for quantum graphs.

We establish the analytic structure of the spectrum of a quantum graph operator as a function of the vertex conditions and other parameters over the whole Grassmannian of possible vertex conditions.
We also discuss the Dirichlet-to-Neumann (DtN) technique of relating quantum and discrete graph operators, which allows one to transfer some results from the discrete to the quantum graph case, but which has issues at the Dirichlet spectrum. We conclude that this difficulty stems from the use of specific coordinates in a Grassmannian and can be easily avoided. Joint work with Jia Zhao (Hebei University of Technology, China)