Explore a 35-minute lecture on time-dependent Hamiltonian simulation of highly oscillatory dynamics presented by Di Fang from the University of California, Berkeley. Delve into the quantum Highly Oscillatory Protocol (qHOP), a novel algorithm designed to handle both large operator norms and rapid changes in time-dependent Hamiltonians simultaneously. Discover how this method achieves superconvergence for digital simulation of the Schrödinger equation, with applications in electronic structure theory, molecular dynamics, and quantum machine learning. Examine topics such as numerical quadrature, complexity analysis, error estimation, and pseudodifferential calculus. Gain insights into the challenges and future directions of this cutting-edge research in quantum numerical linear algebra.