Thematic Seminar: Multimarginal optimal transport, density functional theory, and convex relaxation

Seminar | January 15 | 4:10-5 p.m. | 740 Evans Hall

 Yuehaw Khoo, Stanford University

 Department of Mathematics

Density functional theory is an effective tool in solid state physics and quantum chemistry for electronic structure calculation. However, it has difficulties when dealing with strongly correlated systems. In this talk, we examine the regime where the electrons are strictly correlated. This gives rise to a multimarginal optimal transport problem, a direct extension of the optimal transport problem that has applications in economics and operations research as well. In particular we introduce methods from convex optimization to provide a lower bound to the cost of the multimarginal transport problem with a practical running time. We further propose projection schemes based on tensor decomposition to obtain upper bounds to the energy. Numerical experiments demonstrate a gap of order $10^{-3}$ to $10^{-2}$ between the upper and lower bounds.