Explore the large-coupling strength expansion in Density Functional Theory (DFT) and Hartree-Fock adiabatic connections in this 45-minute lecture by Paola Gori-Giorgi from Vrije Universiteit Amsterdam. Delve into the density fixed adiabatic connection of DFT, connecting the Kohn-Sham determinant with the physical state, and examine its large-coupling strength limit defining a multimarginal optimal transport problem. Investigate the adiabatic connection linking the Hartree-Fock Slater determinant to the physical state, and its relation to Møller-Plesset perturbation theory. Compare and contrast the two large-coupling strength expansions, discussing their applications in improving quantum chemistry approximations. Cover topics such as chemical systems, global interpolation, inequality, and practical results in this comprehensive exploration of advanced concepts in electronic structure theory.