We would like to invite you to the seminar of Quantum Circle ONLINE. Through the Zoom platform will speak Vladimir Lotoreichik on Szegö-type inequality for the 2-D Diracoperator with in nite mass boundary conditions. The seminar takes place on Tuesday, December 8, 2020 from 2.45 pm. The Zoom link, which will allow you to participate in the seminar, can be found on the Quantum Circle website.
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.