Explore the complex world of many-body localization (MBL) in a 45-minute lecture by Piotr Sierant at the International Centre for Theoretical Sciences. Delve into the interpretations of numerical results for MBL, a key topic in the study of quantum matter stability. Gain insights into this branch of non-equilibrium physics, which investigates the behavior of coherent quantum systems under various conditions. Learn about mechanisms constraining many-body dynamics in Hilbert space, including Floquet MBL, Dynamical Freezing, and Hilbert Space Fragmentation. Understand the interdisciplinary nature of this field, drawing from Condensed Matter Physics, Statistical Mechanics, Quantum Field Theory, and Mathematics. Discover the potential applications in quantum technologies and the importance of understanding many-body stability for future quantum devices.