John McGreevy, a physicist at UC San Diego, presents this High Energy Theory Seminar at the Institute for Advanced Study on the entanglement bootstrap, a research program that tries to extract the universal data of quantum many-body systems directly from the local entanglement structure of their ground states. He explains how this data is usually packaged in a quantum field theory, so the bootstrap approach doubles as a new way to learn about QFT itself. The talk works through conditions on the reduced density matrix of a ball region for families of fixed-point states, starting with a review of the topological field theories that govern gapped liquid phases of matter before moving to new results extending the method to conformal field theory in one spatial dimension and above. McGreevy presents joint work with Xiang Li, Ting-Chun Lin, and Rolando Ramirez Camasca, aimed at condensed matter and high energy theorists working on entanglement and field theory.