Gravity from Entanglement in the AdS/CFT correspondence

The AdS/CFT correspondence is a duality between a quantum gravity theory on Anti- deSitter (AdS) space and a conformal field theory (CFT) in one lower dimension. In recent years, it has become clear that the entanglement structure of states in the CFT plays a central role in this duality, as is evident from the Ryu-Takayanagi formula, which states that the entanglement entropy of any subregion in the CFT admits a nice geometric description in the dual gravitation theory in terms of the area of a certain minimal surface. In this talk,we will discuss recent progress in understanding how gravitational dynamics in AdS emerges from the constraints satisfied by the entanglement structure of states in such holographic CFTs. Along the way, we will also mention recently developed techniques for computations of information theoretic quantities such as entanglement entropies and modular Hamiltonians in relativistic quantum field theories. Time permitting, we will also discuss a more fine- grained probe of the entanglement structure called the quantum complexity, which has been conjectured to be a useful probe of certain aspects of the late-time dynamics of general relativity.