Thursday 23 October 2025, 16:00 - 17:00 in HG00.071
Malte Leimbach (Radboud)
Operator system perspectives at truncated noncommutative geometry
A lot of geometric information about a Riemannian (spin^c-)manifold $M$ is encoded in the spectra of the associated Dirac and Laplace operators acting on $L^2(M)$. For instance, it was observed by Connes that the Riemannian distance can be recovered from the Dirac operator together with the *-algebra of smooth functions. In practice, only truncated spectral data might be available, however, and an approach to spectral (noncommutative) geometry based on operator systems rather than *-algebras was put forward by Connes--van Suijlekom to deal with such truncations. In this talk I will give a gentle introduction to operator systems and compact quantum metric spaces, in order to explain some results from my thesis related to convergence of spectral truncations and duality of operator systems. Parts of this are based on joint work with Walter van Suijlekom, and Evgenios Kakariadis and Ivan Todorov.