Explore electron-phonon physics in this 55-minute lecture by Feliciano Giustino from the University of Texas at Austin, presented at IPAM's Model Reduction in Quantum Mechanics Workshop. Delve into topics such as many-body Schrödinger equations, spectral density functions, and electron-phonon matrix elements. Examine real-world examples including the non-adiabatic Kohn anomaly in diamond and electron polarons in LiF. Gain insights into the challenges of Brillouin Zone sampling and phonon-driven electron localization. Discover methods and software used in this field, enhancing your understanding of computational approaches in quantum mechanics and materials science.