How can one define a causal structure or an event horizon in a stringy geometry? In this talk, I will show that this can be done by using the operator algebras of the holographic dual. In particular, I will introduce a new quantity, dubbed "depth parameter", which can be computed in terms of the algebraic structure of the large N boundary theory, and measures a notion of radial extension for the bulk dual of a boundary subregion that still makes sense away from strong coupling. The emergence of a stringy bifurcate horizon requires the depth parameter to be infinite, and the precise value of this depth parameter also allows to diagnose potential violations of the equivalence principle in the bulk at nonzero string length. The depth parameter can be computed in various examples of interest, in particular, it can be used to argue that a sharp horizon structure emerges at high temperature in the bulk dual of N=4 Super-Yang—Mills for all nonzero values of the ’t Hooft coupling.