Theories of hot and dense matter: from hydrodynamics to holography

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As Heraclitus pointed out long time ago, everything flows. In Physics, things which flow are described by fluid dynamics, a collection of equations governing the flow in a precise mathematical sense. Many different physical systems may flow in the same way, as determined by the symmetry of their microscopic constituents. A simple example would be the flow of a gas and of a normal fluid. Less common examples may involve the relativistic symmetry that governs the behaviour of matter which moves at speeds close to the speed of light: that symmetry ensures that certain atomic gases, quantum magnets, and the quark-gluon plasma of the early Universe obey the same fluid-dynamical laws. Several years ago, it was understood that black holes may also flow, in exactly the same way liquids do. Thus the study of fluid dynamics translates to the study of black hole dynamics, and vice versa. The liquids relevant to this black-hole/fluid correspondence are highly quantum-mechanical, and seem to flow in virtually the same way as the quark-gluon plasma created at the Relativistic Heavy Ion Collider in Brookhaven, and at the Large Hadron Collider at CERN. This connection between black holes and quantum liquids combined with the renewed interest in relativistic hydrodynamics due to the experimental heavy-ion program has recently led to important progress in the field as old as classical fluid dynamics. This proposal will focus on understanding hot and dense relativistic matter, and on connecting its mathematical description with black hole physics. The questions to be explored include macroscopic fluid flows, thermal and quantum fluctuations, correlations, quantum-mechanical anomalies, matter in external fields, and the associated physical effects.