The spectral localiser: what and whyOberseminar Global Analysis and Operator Algebras

by Yuezhao Li (MPIM Bonn)

Tuesday Apr 28, 2026, 2:15 PM → 3:45 PM Europe/Berlin

Endenicher Allee 60/1-008 (Mathezentrum)

The spectral localiser method, introduced by Loring and Schulz-Baldes, allows for computing the index pairing between a K-theory class and a spectral triple by means of (the signature of) a finite-dimensional matrix, which is supported on a finite spectral truncation. In recent years, bivariant K-theoretic methods have been employed to provide new insights into their construction. This allows for generalisation to the Hilbert module setting.

The goal of this talk is to give an introduction to the spectral localiser and highlight its interpretation in bivariant K-theory. I will also discuss some subtleties that arise while working with Hilbert modules.