Explore numerical analysis techniques for Hamiltonian simulation and learning in this 52-minute lecture presented by Di Fang from Duke University at IPAM's Tensor Networks Workshop. Delve into two crucial aspects of quantum information science: simulating Hamiltonian dynamics and learning Hamiltonian structures. Examine methods to mitigate the strong operator norm dependence in quantum dynamics simulation accuracy, with a focus on the semiclassical Schrödinger equation. Discover the groundbreaking algorithm achieving the Heisenberg limit for efficiently learning interacting N-qubit local Hamiltonians. Gain insights into the challenges and advancements in quantum information processing and computational methods for complex quantum systems.