Srdečně vás zveme na další seminář v rámci Kvantového kroužku ONLINE. Prostřednictvím platformy Zoom bude hovořit Vladimir Lotoreichik na téma Szegö-type inequality for the 2-D Diracoperator with in nite mass boundary conditions. Seminář se koná v úterý 8. 12. 2020 od 14.45 hod. Zoom-ové souřadnice, které vám umožní se semináře zúčastnit, najdete na webu Kvantového kroužku.
Abstract:
In this talk, we will discuss spectral features of the Dirac operator within nite mass boundary conditions in a smooth bounded domain of R2. Motivated by spectral geometric inequalities, we derive a non-linear variational formulation to characterize its principal eigenvalue. This characterization turns out to be very robust and allows for a simple proof of a Szegö type inequality as well as a new reformulation of a Faber-Krahn type inequality for this operator. We will also present strong numerical evidence supporting the validity of a Faber-Krahn type inequality. This talk is based on a joint work with Pedro Antunes, Rafael Benguria,and Thomas Ourmiéres-Bonafos.