Explore recent advancements in accelerating Density Functional Theory (DFT) calculations using hybrid functionals in this 51-minute lecture by Lin Lin from the University of California, Berkeley. Delve into the challenges of solving Hartree-Fock-like equations and examine the finite-size effects in periodic systems. Gain insights into fast algorithms, adaptive compression techniques, and convergence rates for large-scale hybrid DFT functionals. Understand the global convergence properties, fog exchange energy, and finance side effects associated with these calculations. Analyze the main results, including quadratic error forms and sharpness in the context of quantum mechanics. This talk, presented at IPAM's Large-Scale Certified Numerical Methods in Quantum Mechanics Workshop, offers a comprehensive overview of cutting-edge research in computational quantum chemistry.