Aspects of the Bosonic Spectral Action

Explore a 42-minute lecture on noncommutative spectral geometry and its applications in cosmology. Begin with a brief introduction to the subject before delving into the cosmological implications of applying the spectral principle to almost commutative manifolds. Learn how astrophysical data can be used to constrain one of the three cutoff momenta in the asymptotic expansion of the cutoff bosonic spectral action. Investigate the role of scalar fields within this context. Address issues of renormalisability, ultraviolet completeness, and spectral dimensions by examining an alternative definition of the bosonic spectral action based on zeta function regularisation. This talk, presented by Mairi Sakellariadou at the Hausdorff Center for Mathematics, was part of the Hausdorff Trimester Program on Non-commutative Geometry and its Applications.