MCS-MP Seminar: Sabine Boegli

Speaker: Sabine Boegli (Durham)

Title: On the number of discrete eigenvalues of Schrödinger operators with complex potentials

Abstract: For Schrödinger operators with complex-valued L^p potentials, we will present an upper bound on the number of discrete eigenvalues in half-planes separated from the positive real axis. This is a generalisation of the celebrated Cwikel-Lieb-Rozenblum (CLR) inequality to complex potentials. As a consequence, we derive new Lieb-Thirring type inequalities and we discuss their optimality.