Title: Mathematical problems and numerical methods in first-principle molecular simulation
Abstract: First-principle molecular simulation based on electronic structure calculation has become an essential tool in chemistry, condensed matter physics, molecular biology, materials science, and nanosciences. It is also an inexhaustible source of exciting mathematical and numerical problems. In this talk, I will focus on Density Functional Theory and the Kohn-Sham model, which is to date the most widely used approach in electronic structure calculation, as it provides the best compromise between accuracy and computational efficiency. I will present some recent progress made in the mathematical understanding and the numerical analysis of this model, which pave the road to high-fidelity numerical simulations (with a posteriori error bounds) of the electronic structure of large molecular systems. I will then discuss the difficult issue of coupling the Kohn-Sham model with coarser models in view of simulating even larger molecular systems, such as drug-protein complexes in solution.