Noncommutative Geometry Seminar

In this talk, I will begin with a review of p-adic numbers and their relation to the Bruhat-Tits tree, an infinite regular graph. A bulk/boundary correspondence can be naturally set up, with the boundary theory defined on a p-adic number field (instead of real numbers in standard Archimedean AdS/CFT constructions) and the bulk described by the Bruhat-Tits tree whose boundary is precisely the p-adic numbers. I will give an introduction to p-adic AdS/CFT, and discuss holographic correlation functions, emphasising the surprising similarities between the p-adic and Archimedean results, when correlation functions are expressed in terms of local zeta functions. I will end with a brief discussion of edge-length dynamics and a discrete analog of Einstein equations, based on a notion of Ricci curvature on graphs.