Kohn-Sham models (mathematical) Carlos Garcia-Cervera University of California, Santa Barbara (UCSB) Mathematics • Thomas-Fermi and Orbital-free DFT. • Hohenberg-Kohn DFT: v-representability. • N-representability and the Levy-Lieb formulation. • Kohn-Sham DFT. • The Janak functional: Density matrices and extended Kohn-Sham.