Quantum field theory in a non-commutative space: theoretical predictions and numerical results on the fuzzy sphere.
Quantum gravity: unification of principles and interactions, and promises of spectral geometry.
Quantum isometry group for spectral triples with real structure.
Quantum ultrametrics on AF algebras and the Gromov-Hausdorff propinquity
We construct quantum metric structures on unital AF algebras with a faithful tracial state, and prove that for such metrics, AF algebras are limits of their defining inductive sequences of finite-dimensional C*-algebras for the quantum propinquity. We then study the geometry, for the quantum propinquity, of three natural classes of AF algebras equipped with our quantum metrics: the UHF algebras, the Effrös-Shen AF algebras associated with continued fraction expansions of irrationals, and the Cantor...