UBC Math Department Seminar: Muhammad Hassan

From explaining the complex mechanisms underlying the light-harvesting chlorophyll molecule to understanding the origin of superconducting in novel 2D materials, an incredible range of scientific phenomena are governed by interacting systems of electrons. Unsurprisingly there-fore, the study of such systems– known as electronic structure theory– has a wide domain of applications from drug discovery and the creation of new compounds for sustainable energy and green catalysis to the design of so-called quantum materials with exotic magnetic, ferroelectric, or superconducting properties.

In this talk, I will present an overview of one of the central problems in electronic structure theory, namely, the computation of the lowest energy state– or ground-state– of an electronic system and the various connections of this problem with numerical analysis, partial differential equations, high-dimensional approximations, and differential geometry. I will focus primarily on two popular methodologies for the numerical resolution of the ground state, namely, wave-function methods and Kohn-Sham density functional theory. I will discuss advances in the mathematical analysis of these methodologies, a few outstanding open questions, and some trends going forward.