Advances in Spectral Theory for Non-Selfadjoint Operators

IAS Visiting Fellow Dr Petr Siegl delivers a seminar on their research - 

Many physical systems can be described by partial differential equations which in turn generate operators between Banach spaces. A well-known illustration of such interplay is quantum mechanics together with the spectral theory of self-adjoint operators in a Hilbert space. However, in several branches of physics like hydrodynamics, damped systems, quantum resonances, superconductivity or balanced loss/gain materials, the occurring PDEs contain non-symmetric terms and thus lead to non-self-adjoint operators. 

Due to the lack of powerful self-adjoint tools like the spectral theorem or variational principles, the encountered phenomena are very different from the self-adjoint case and include spectral instabilities, divergence of expansions in eigenvectors or non-reliability of approximations. In the first part of the talk, we give an introduction in the non-self-adjoint aspects of spectral theory. In the second part, we present new results on the convergence of the expansions in eigenvectors based on the local form subordination.

Arrivals from 11:45 am for a 12:00 noon start. For those joining in-person, lunch will be served after the seminar from 1:00pm.

This event is hybrid format, please use the required booking button at the bottom of the page to choose either in-person or online attendance.
(Please note that in-person spaces are limited and booking is required, so we can manage numbers for catering and also the space in the seminar room)

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