Explore reparametrization invariance and its applications in a 42-minute lecture by Jorge Kurchan at the International Centre for Theoretical Sciences. Delve into the connections between glasses and toy black holes as part of the program on Stability of Quantum Matter in and out of Equilibrium at Various Scales. Gain insights into many-body quantum systems, coherent time evolution, and the stability of quantum matter under external drives. Examine mechanisms constraining many-body dynamics in Hilbert space, including Many-body localization, Floquet MBL, Dynamical Freezing, and Hilbert Space Fragmentation. Learn about the interdisciplinary nature of this research, drawing from Condensed Matter Physics, Statistical Mechanics, Quantum Field Theory, and Mathematics. Discover the implications for quantum devices and controlling quantum systems, making this lecture relevant for researchers in quantum technologies and related fields.