Explore the concept of dynamical freezing and emergent conservations in interacting systems in this 28-minute lecture by Arnab Das from the International Centre for Theoretical Sciences. Delve into the stability of quantum matter in and out of equilibrium at various scales, examining mechanisms that constrain many-body dynamics in Hilbert space. Learn about phenomena such as Many-body localization, Floquet MBL, and Hilbert Space Fragmentation, and their potential to underpin novel phases of quantum matter. Gain insights into the interdisciplinary nature of this research, drawing from condensed matter physics, statistical mechanics, quantum field theory, and mathematics. Understand the practical implications for quantum device stability and control, relevant for researchers working on quantum technologies.