## Details

The AdS/CFT conjecture in physics posits the existence of a

correspondence between gravitational theories in asymptotically Anti-de

Sitter (aAdS) spacetimes and field theories on their conformal boundary.

In this presentation, we prove a rigorous mathematical statement toward

this conjecture in the classical relativistic setting.

In particular, we show there is a one-to-one correspondence between aAdS

solutions of the Einstein-vacuum equations and a suitable space of data

on the conformal boundary (consisting of the boundary metric and the

boundary stress-energy tensor), provided the boundary satisfies a

geometric condition. We also discuss applications of this result to

symmetry extension, as well as its connection to unique continuation

problems.

This is joint work with Gustav Holzegel, and makes use of joint works

with Alex McGill and Athanasios Chatzikaleas.