  We study the caustics on the boundaries of entanglement wedges in the context
of holography in asymptotically AdS$_3$ spacetimes. These entanglement wedges
play an important role in our understanding of the emergence of bulk locality.
A procedure was proposed by Sanches and Weinberg [arXiv:1703.07780] for
identifying boundary operators which are local in the bulk, which also applies
to certain regions that lie beyond the reach of HRT surfaces by taking
advantage of the lightsheets which bound entanglement wedges. We identify the
caustics which terminate these lightsheets in conical deficit and BTZ black
hole spacetimes and find that in some examples these caustics lead to a sharp
corner in the entanglement wedge. The unexpected shape of these entanglement
wedges leads, in those cases, to a breakdown of this procedure. Many of the
properties of the rich variety of caustics possible in higher dimensions
remains to be explored which, as this work demonstrates, could lead to more
unexpected features in the shapes of entanglement wedges.
