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Explore the fascinating intersection of holography and hydrodynamics in this comprehensive lecture delivered at the International Centre for Theoretical Sciences. Delve into the profound connections between string theory's AdS/CFT correspondence and fluid dynamics, where black hole geometries map onto relativistic Navier-Stokes equations through the fluid-gravity duality. Discover how thermal relaxation processes correspond to quasi-normal mode decay and how entanglement growth manifests as geometric surface evolution. Learn about the revolutionary insights that emerge when gravitational theories in higher dimensions are used to understand strongly coupled quantum field theories and their hydrodynamic behavior. Examine the mathematical frameworks that connect black hole physics to fluid mechanics, revealing deep universal principles governing nonequilibrium thermodynamics. Understand how holographic techniques provide powerful tools for analyzing transport phenomena, thermalization processes, and the emergence of classical hydrodynamic behavior from quantum systems. Gain insights into cutting-edge research that bridges classical statistical physics, quantum many-body systems, and string theory approaches to understanding complex fluid dynamics and nonequilibrium phenomena.
