Dhumuntarao, Aditya2023-11-282023-11-282023-06https://hdl.handle.net/11299/258726University of Minnesota Ph.D. dissertation. June 2023. Major: Physics. Advisor: Joseph Kapusta. 1 computer file (PDF); xi, 203 pages.We explore the intersections between classical gravity and quantum information via holographic dualities. Such dualities provide a sophisticated mathematical dictionary which encodes information from a d-dimensional quantum theory onto a (d+1)-dimensional theory of gravity via equivalence of their partition functions. In this dissertation, we bridge geometry and quantum information in three parts. In Part I, we elucidate the connection between geometry and thermodynamics. Using the laws of black hole thermodynamics, we prove the existence of novel liquid-gas phase transitions in the phase diagram for lower dimensional AdS black holes. We further establish a proof that thermodynamic instabilities for AdS uniform black strings are correlated with classical gravitational instabilities. In Part II, we focus on applications of holographic quantum/classical dualities. Specifically, we study putative gravitational duals to 4d SU(N_c) Yang-Mills under various deformations. First, we demonstrate that deforming the bulk gravity dual with codimension one branes yields a scalar mass spectra concordant with lattice data at zero temperature. Next, at finite temperature, we show the presence of such branes imposes an upper bound on the thermal Bekenstein-Hawking entropy. We further prove that deforming the R-charge for 4d N=4 Super Yang-Mills on S^1_\beta\times S_R^3 avoids the deconfinement/Hagedorn phase transition at weak coupling and the Hawking/Page phase transition at strong coupling. These results connect quantum statistical systems and equilibrium gravitational systems. In Part III, we link quantum information and classical geometry holographically. Using geometric flows of extremal surfaces in asymptotically AdS spacetimes, we prove novel speed limits on the growth of entanglement entropy, equal time correlators, and spacelike Wilson loops for strongly coupled, far from equilibrium quantum systems admitting holographic duals. Our results imply new bounds on the entanglement velocity, prove the entanglement tsunami conjecture for a large class of states in 2d, and uncover a new momentum-entanglement correspondence, proving that entanglement growth is directly related to the momentum flux crossing an extremal surface.enBlack HolesClassical GeometryEntanglement EntropyHolographyQuantum Field TheoryQuantum InformationThesis or Dissertation