The properties of some simple non-selfadjoint models, such as the complex Airy operator, Davies operator or the complex cubic oscillator, have been recently investigated in order to highlight some surprising properties of non-selfadjoint (non-normal) operators. For instance, the so-called Davies operator has played an important role in the understanding of the spectral instability phenomenon. In this talk, we will recall the main spectral and pseudospectral properties of these models, and then present a wide range of applications, including problems arising from non-hermitian quantum mechanics, control theory or superconductivity.

Due to technical problems with the microphone, the sound of this video may be partially or completely scrambled, we apologize for this.