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The Nobel Prize in Physics 2016 was awarded to David J. Thouless, F. Duncan M. Haldane and J. Michael Kosterlitz "for theoretical discoveries of topological phase transitions and topological phases of matter". Their work starting in the early 1970s and continuing into the 1980s on phase transitions in two dimensional systems, one dimensional spin chains and the integer quantum Hall effect using topological concepts laid the foundation for the discovery of new classes of topological quantum materials.
In the last ten years the search for new topological states of matter has intensified and is currently one of the hottest areas of research in all of physics. New topological materials such as topological insulators and superconductors and potential applications such as topological quantum computing are all the rage. In this lecture I will outline the research recognized by the 2016 Nobel Prize and make the connection to current research on topological insulators. The presentation aims to make this fascinating research accessible to a broad audience, however occasionally some references to basic concepts from quantum mechanics, statistical mechanics and condensed matter theory at an advanced undergraduate level will be unavoidable.