The noncommutative integral is a functional identified by Connes as an analogy of the integral with respect to the Riemannian volume form given in terms of spectral data. While investigating means of computing Connes' integrals in terms of spectral truncations, we came across some interesting links to quantum ergodicity. It turns out that Connes' geodesic flow fits nicely into the framework of C*-dynamical systems. Based on joint work with Eva-Maria Hekkelman.

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