Explore KPZ physics in integrable spin chains through this 38-minute lecture by Abhishek Dhar from the International Centre for Theoretical Sciences. Delve into the stability of quantum matter in and out of equilibrium at various scales, part of a comprehensive program examining many-body quantum systems with coherent time evolution. Gain insights into mechanisms constraining many-body dynamics in Hilbert space, including Many-body localization, Floquet MBL, Dynamical Freezing, and Hilbert Space Fragmentation. Learn about the interdisciplinary approach drawing from Condensed Matter Physics, Statistical Mechanics, Quantum Field Theory, and Mathematics to understand many-body stability problems. Discover the relevance of this research for developing stable quantum devices and enhancing control over quantum systems.