A compact manifold can be described through a spectral triple, consisting of a Hilbert space H, an algebra of functions A and a Dirac operator D. But what if we are given a spectral triple? Then the situation is more complicated, it is not clear how to reconstruct geometry from a spectral triple, in particular one with a non-commutative algebra A, or a finite Hilbert space H. But these are questions one would like to ask if trying to use spectral triples to possibly quantize gravity. In this talk I will show how we recover metric information from a truncation of a spectral triple to make an image, and show some odd shrinking spectral triples.
This video was produced by the University of Münster, and forms part of the workshop Non-commutative geometry meets topological recursion.
