The research in the Seradjeh group focuses on topological aspects of electronic properties of solids and other materials. This research encompasses several systems, under the name topological insulators and topological superconductors, and is at the frontier of condensed matter physics today. To describe these systems, we use modern theories of quantum mechanics and relativity, combined with mathematical notions of topology to understand and uncover spectacular phenomena, such as fractional charge, emergent magnetic monopoles, emergent Majorana fermions, and applications in quantum computation and beyond. The students in this project will investigate aspects of model topological insulators and superconductors by employing analytical and simple numerical methods using Mathematica, Matlab, or C/C++/Fortran. The problems are designed to understand the fundamental principles governing the systems, their connection to experiments, and potential applications and architectures for novel devices. The student will become familiar with relevant experiments, will learn the underlying concepts and a selection of theoretical and numerical techniques.