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Explore the intersection of inverse scattering methods and Macroscopic Fluctuation Theory in this comprehensive 2-hour lecture delivered at the International Centre for Theoretical Sciences. Delve into advanced mathematical frameworks that bridge quantum and classical nonequilibrium systems, examining how inverse scattering techniques can be applied to understand large deviation principles and thermodynamic fluctuations in stochastic processes. Learn about the theoretical foundations that connect integrable quantum systems with classical fluctuating hydrodynamics, and discover how these mathematical tools provide insights into transport phenomena and current fluctuations across different physical contexts. Gain understanding of the sophisticated mathematical machinery underlying modern approaches to nonequilibrium statistical mechanics, including the role of exact solvability in revealing universal structures in both quantum and classical many-body systems. This lecture forms part of a specialized workshop bringing together perspectives from classical statistical physics, quantum many-body theory, and string theory approaches to hydrodynamics and fluctuation phenomena.
