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.