Our research is centered on the rigorous mathematical study of properties of electron systems, mainly with Coulomb interaction. Specifically, we are mostly interested in atoms and molecules in the clamped-nuclei approximation. Selected topics are regularity of exact eigenstates, and of solutions of effective models, such as Hartree-Fock theory, and various questions in spectral asymptotics.The research pertains to both non-relativistic and certain (pseudo)relativistic systems.
One main field of interest is the precise description of the behaviour of exact eigenstates of the full N-particle problem at the singularities of the many-body potential, beyond Kato's Cusp Condition, and its consequences for the behaviour of the corresponding electron density.
Another related topic is the regularity of solutions when the non-relativistic kinetic energy is replaced with a (pseudo)relativistic one, expressed by a non-local operator given by Einstein's energy relation. Similar questions are being investigated for solutions to Hartree-Fock and other mean field models, in both the non-relativistic and relativistic case.
Another field of interest is the study of various spectral asymptotics in the (pseudo)relativistic setting, both for Coulombic systems and for a (non-interaction) free electron gas in a bounded domain.