Mathematics Colloquia and Seminars

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Over the last few years it has become clear that there is a deep connection between quantum entanglement and gravity. I will talk about two aspects of this connection. The first involves understanding quantum entanglement from a geometric perspective in the context of gauge/gravity duality. After reviewing the remarkably simple prescription of Ryu and Takayanagi, I will propose a general formula for entanglement entropy in theories dual to higher derivative gravity. I will also give a new geometric formulation of Renyi entropy, and outline a derivation of the Hubeny-Rangamani-Takayanagi conjecture. The second aspect of the connection involves understanding the emergent nature of spacetime as a quantum error correcting code. This new perspective gives a precise formulation of the "subregion-subregion" duality in AdS/CFT, and clarifies the limits of its validity.