Strongly-Disordered Topological Insulators

Seminar in Mathematics

Topological insulators are novel materials which insulate in their bulk, yet, along their boundary are excellent conductors. Their exotic properties are explored by identifying the topological space of quantum mechanical Hamiltonians and calculating its set of path-connected components, which in interesting cases, has more than one component. The components induce a topological invariant which corresponds to an experimentally measurable physical quantity. In this talk I will focus on such systems in the regime of strong disorder, which leads to rich problems in analysis and probability.