Serge Nicaise: Spectral analysis of second order operators with sign-changing coefficients on graphs

Abstract: The study of diffusion problems with sign changing coefficients increased recently because these problems appear in several areas of physics, for example in electromagnetism. Thus some mathematical and numerical investigations have been performed for domains of the plane or of the space.

Similar questions were recently considered on graphs. The goal of this talk is to present some results on arbitrary compact graphs with Kirchhoff interior vertex conditions and, as much as possible, variable coefficients.