mSPACE Lumer Lectures
This series of lectures is named after Günter Lumer, a great mathematician with extensive achievements and a deep curiosity for differential equations, operator theory, and their applications. It is a joint scientific activity of the Action’s four Working Groups. The lectures will be delivered by distinguished scientists whose research interests are related to the Action. All past lectures can be viewed on.
Lumer Lecture by Serge Nicaise
Host: WG1
Date: 17 February 2026, 15:00 CET.
Title: Forty years of spectral theory on metric graphs
Abstract:
First, I will make a short introduction on Lumer’s life and career. I will recall some ”old” results on spectral theory on finite graphs, like characterization of the spectrum, spectral gaps, asymptotic behaviors and Weyl’s formula. I will finally mention some recent results for infinite graphs and indefinite operators. The main tools are the use of the fundamental solutions of the ODE and some algebraic manipulations, the min-max principle and the knowledge of the eigenvalues in some particular cases.
Lumer Lecture by Marco Marletta
Host: WG2
Date: 22 April 2026, 16:00 CET.
Title: Essential numerical ranges for unbounded operators & pencils, with applications to PDEs
Abstract:
This talk gives an introduction to essential numerical ranges for unbounded linear operators and (mostly linear) pencils and explain how they can be used to get a priori estimates on where the spectra of operators lie, and where spectral pollution might lie if we attempt to use numerical approaches to find spectra. The work is joint with S. Boegli, F. Ferraresso and C. Tretter; some of the applications build on earlier work with G. Alberti, B.M. Brown and I. Wood.