Explore a 28-minute lecture from the Indo-French workshop on Classical and Quantum Dynamics in Out of Equilibrium Systems, focusing on dynamical phases in non-equilibrium conformal field theories. Delivered at the International Centre for Theoretical Sciences' Ramanujan Lecture Hall in Bengaluru, learn about cutting-edge research in classical and quantum out-of-equilibrium dynamics. Part of a broader initiative to strengthen Indo-French academic collaboration, the lecture contributes to a workshop covering topics including non-equilibrium statistical physics, quantum many-body systems, long-range interactions, quantum resetting, generalized Gibbs ensembles, phase space quantum dynamics, and quantum measurement theory. Gain insights from this CEFIPRA-supported academic exchange program designed to foster international research partnerships and scientific cooperation between France and India.