Topology and Superconductivity In and Out of Equilibrium

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The field of condensed matter physics is concerned with understanding and controlling the properties of materials. Material properties are determined by the microscopic components of matter - electrons and atoms. The microscopic world is governed by the laws of quantum mechanics, rather than classical mechanics and is described mathematically with tools specifically developed for systems of many particles (of the order of 10^22 atoms per cubic cm). Such tools have existed for over 60 years and have been very successful in predicting properties like conduction and magnetism from microscopic considerations. In particular, Landau's Fermi liquid theory describes the electrons as they move through an ordered lattice of atoms. In this framework very general arguments allow physicists to classify states of matter and study transitions between different states.