first proposed that the model is holographically dual to quantum gravity on AdS2, and identified its low temperature entropy with the Bekenstein–Hawking black hole entropy. Unlike previous models of quantum gravity, it appears that the SYK model is solvable in a regime which accounts for the subtle non-thermal correlations in the Hawking radiation. One-dimensional quantum systems with an energy gap Sachdev and collaborators developed a formally exact theory for the non-zero temperature dynamics and transport of one-dimensional quantum systems with an energy gap. The diluteness of the quasiparticle excitations at low temperature allowed the use of semi-classical methods. The results were in good quantitative agreement with NMR and subsequent neutron scattering observations on S=1 spin chains, and with NMR on the Transverse Field Ising chain compound CoNb2O6 Quantum impurities The traditional Kondo effect involves a local quantum degree of freedom interacting with a Fermi liquid or Luttinger liquid in the bulk. Sachdev described cases where the bulk was a strongly-interacting critical state without quasiparticle excitations. The impurity was characterized by a Curie susceptibility of an irrational spin, and a boundary entropy of an irrational number of states. Ultracold atoms Sachdev predicted density wave order and 'magnetic' quantum criticality in tilted lattices of ultracold atoms. This was subsequently observed in experiments. The modeling of tilted lattices inspired a more general model of interacting bosons in which a coherent external source can create and annihilate bosons on each site. This model exhibits density waves of multiple periods, along with gapless incommensurate phases, and has been realized in experiments on trapped Rydberg atoms. Metals with fractionalization and emergent gauge fields Sachdev and collaborators proposed a new metallic state, the fractionalized Fermi liquid (FL*): this has electron-like quasiparticles around a Fermi surface, enclosing a volume distinct from that required by Luttinger's theorem. A general argument was given that any such state must have very low energy excitations on a torus, not related to the low energy quasiparticles: these excitations are generally related to the emergent gauge fields of an associated spin liquid state. In other words, a non-Luttinger Fermi surface volume necessarily requires topological order. The FL* phase must be separated from the conventional Fermi liquid (FL) by a quantum phase transition; this transition need not involve any broken symmetry, and examples were presented involving confinement/Higgs transitions of the gauge field. Such a quantum phase transition has been observed in CeCoIn5. Quantum critical transport