The spectral localiser via E-theoryOberseminar Global Analysis and Operator Algebras

by Yuezhao Li (Uni Leiden)

Tuesday Nov 18, 2025, 2:15 PM → 3:45 PM Europe/Berlin

Endenicher Allee 60/1-008 (Mathezentrum)

Terry Loring and Hermann Schulz-Baldes have introduced the
spectral localiser as a means to compute the index pairing between a
K-theory class and a spectral triple. The spectral localiser is a
finite-dimensional, invertible matrix that is supported on a finite
spectral subspace of the spectral triple. In the odd case, we interpret the
spectral localiser as an index pairing in E-theory. Namely, the image of an
odd K-theory class under the asymptotic morphism generated by an odd
spectral triple.  This allows for speaking of spectral truncations of index
pairings in the framework of bivariant K-theory. This is based on joint
work with Bram Mesland.