Abstract: 

The eta invariant is a spectral invariant defined using the spectrum of a Dirac operator. it appears as the boundary correction term in the Atiyah-Patodi-Singer index theorem. I'll discuss some interesting decompositions of eigenfunctions for Dirac operators on cones, which come from lifting the spectral asymmetry in the eta invariant to the level of eigenvectors. Based on Reference: https://arxiv.org/abs/2603.26057