Mathematical Challenges in Density Functional Theory
Schrödinger's equation fits on just one line and it is supposed to accurately describe the behavior of most atoms and molecules of our world. But it is essentially impossible to simulate to a high precision, due to its very high dimensionality.
In this talk I will give a general overview of Density Functional Theory (DFT), which is the main technique used nowadays to approximate Schrödinger's equation for electrons.
I will then discuss the mathematical structure of DFT and mention a few results obtained in collaboration with Elliott Lieb and Robert Seiringer