Explore a 42-minute lecture on low rank approximation techniques in electron excitation calculations, presented by Chao Yang from Lawrence Berkeley National Laboratory at IPAM's Large-Scale Certified Numerical Methods in Quantum Mechanics Workshop. Delve into the practical approach of using Kohn-Sham density functional theory for ground state calculations, followed by solving Dyson's equation for Green's functions. Discover how the interpolative separable density fitting (ISDF) technique can significantly reduce computational costs in post-DFT calculations. Examine the effectiveness of low rank approximation in these calculations and learn about the accuracy and efficiency of this approach. The lecture covers topics such as the quantum many-body problem, Lehmann representation, BSE Hamiltonian, integral computation, ISDF implementation, and its application to both periodic and non-periodic systems.