Description
In this talk we will explore path integrals over finite spectral triples as models of Euclidean Quantum Gravity, first proposed by J. W. Barrett. Such integrals can be expressed as bi-tracial multi-matrix integrals. The Feynman diagrams of these integrals are decorated maps, and they satisfy their own Schwinger-Dyson equations which are generalizations of Tutte's recursion. I will outline how recent work has used map enumeration techniques to solve these models explicitly.
