Webinar invitation: Hidden symmetries in non-self-adjoint graphs

Many institutions worldwide have moved their usual seminar series with guest lecturers to the cyberspace, allowing a wide audience of researchers and enthusiasts to attend interesting webinars. Before the summer break, we shared Stefan Teufel's virtual talk at FernUni Hagen with the members of our Action, and almost 50 of us participated in the webinar.

With the new academic year, we continue this practice, and our Prof Delio Mugnolo invites all interested researchers to attend the webinar by Dr. Amru Hussein from Kaiserslautern:

Hidden symmetries in non-self-adjoint graphs

(September 3, 2020 at 2pm CEST)

Abstract: On a finite metric graphs one can consider all realizations of the Laplace operator in L²-spaces. These are defined by boundary conditions, and here the question is discussed how these general – mostly non-self-adjoint boundary conditions – can be studied in a systematic way. The approach advocated here is centered around the Cayley transform of the boundary conditions which in the self-adjoint case has the interpretation of alocal scattering matrix. These Cayley transforms encode several spectral properties of the corresponding Laplace operators, and therefore studying these Cayley transforms exposes some previously hidden symmetries of these Laplace operators. In particular thereby the generators of C₀- and analytic semigroups, and C₀-cosine operator function can be characterized. On star-shaped graphs a characterization of generators of bounded C₀-groups and thus of operators similar to self-adjoint ones can be obtained. This will be illustrated by several examples.

You can access the webinar via Zoom, using the link below:

https://fernuni-hagen.zoom.us/j/98671479998?pwd=U1hxUDFyL2lTa1RqNXkyWnZZMzB0UT09

Meeting ID: 986 7147 9998
Passcode: NVH=0!Gn