| Résume | I will give a light introduction to the theory of quantum graphs and some related operator algebraic constructions. Quantum graphs are generalizations of directed graphs within the framework of non-commutative geometry, and they arise naturally in a surprising variety of areas including quantum information theory, representation theory, and in the theory of non-local games. I will review the well-known construction of Cuntz-Krieger C*-algebras from ordinary graphs and explain how one can generalize this construction to the setting of quantum graphs. Time permitting, I will also explain how quantum symmetries of quantum graphs can be used to shed some light on the structure of quantum Cuntz-Krieger algebras. (This is joint work with Kari Eifler, Christian Voigt, and Moritz Weber.) |
