Topics of current research include developing methods for large-scale electronic structure calculations, including real-space methods and reduced-order scaling algorithms for large-scale Kohn-Sham DFT and time-dependent DFT calculations, tensor structured techniques for electronic structure calculations, and development of methods and algorithms for all-electron DFT and TDDFT calculations. Other areas of research interest include multi-scale methods for density-functional theory (electronic structure) calculations, electronic structure studies on defects in materials, quasi-continuum method, analysis of approximation theories, numerical analysis, and quantum transport in materials.