Erik Waldemarson will defend his Master thesis “Index theorems with spectral localizers”.

Supervisor: Magnus Goffeng
Examiner: Mikael P Sundqvist

Abstract:
The Atiyah-Singer index theorem is a foundational result in mathematics, providing a deep connection between the analytical properties of an elliptic differential operator and the topological properties of its underlying manifold. This thesis focuses on a numerical approach to index theory for generalized Toeplitz operators. Building on the work of Loring and Schulz-Baldes, we utilize the spectral localizer method, which relates the analytical index of a Toeplitz operator to the signature of an associated finite-dimensional matrix, the spectral localizer. The contributions of this work are a simplified proof of the key formula, and new, less restrictive parameter bounds.

Zoom link: https://lu-se.zoom.us/j/65058482464