The research focuses on two general topics in theoretical condensed matter physics and chemical physics. The first problem is the mathematical description of electron transport in low temperature disordered solids and, in particular, the description of the metal-insulator transition in interacting disordered Fermi liquids. The second research topic is on the glassy state as a liquid is cooled or quenched. Of particular concern is the understanding of the dramatic increase in the viscosity in the glass transition region.