Explore the dynamical manifestations of many-body quantum chaos and self-averaging in this 39-minute lecture by Lea Santos from the International Centre for Theoretical Sciences. Delve into the stability of quantum matter in and out of equilibrium at various scales, examining coherent time evolution in experimentally realizable many-body quantum systems. Investigate mechanisms constraining many-body dynamics in Hilbert space, including Many-body localization (MBL), Floquet MBL, Dynamical Freezing, and Hilbert Space Fragmentation. Gain insights into novel phases of quantum matter and their potential applications in quantum devices. Learn how this interdisciplinary field draws from Condensed Matter Physics, Statistical Mechanics, Quantum Field Theory, and Mathematics to address fundamental questions about quantum system stability and control.