Lectures by Michael Björklund, Per Salberger and Magnus Goffeng
Overview
- Date:Starts 9 June 2023, 13:10Ends 9 June 2023, 16:05
- Location:Pascal, Hörsalsvägen 1
- Language:English and Swedish
13.10–14.00 Michael Björklund, Presentation of the scientific results of this year's Wallenberg Awardee: Olof Sisask
14.10–15.00 Per Salberger, Presentation of the scientific results of this year's Wallenberg Awardee: Lilian Matthiesen
15.15–16.05 Magnus Goffeng (Wallenberg Awardee 2021): Counting negative eigenvalues with index theory.
Abstract: In this talk we will consider the Pauli Hamiltonian, a Schrödinger operator describing a spin particle moving in a magnetic field in two dimensions. The problem we will discuss is that of describing how many negative eigenvalues there are for its Neumann realization on a compact domain. We provide a sharp lower bound for the number of negative eigenvalues by means of a connection to Atiyah-Patodi-Singer’s index theorem for Dirac operators arising from an elementary integration by parts. We conclude a new asymptotic formula for the counting function of the semiclassical Landau-Neumann Hamiltonian. Joint work with Søren Fournais, Ayman Kachmar and Mikael Persson-Sundqvist.
