In this course, we will prepare you to dive into the exciting research topic of topological phases of matter. As recognised by the 2016 Nobel Prize for Physics, this field focuses on how beautiful ideas from mathematics have been able to revolutionise our understanding of quantum systems.
Beginning from elementary quantum physics, we shall show how the geometrical and topological properties of wave functions can play an important role in physical phenomena, such as the famous integer quantum Hall effect. In the initial lectures of our course, you will become familiar with key concepts including the Berry phase, Chern number and bulk-edge correspondence. Building on this, we will then introduce you to the major new developments in the field since 2005, including the discovery of topological insulators, topological superconductors and Weyl semimetals. In addition to more conventional electronic systems, we shall also cover exciting recent advances in engineering topology for photons and ultracold atoms. In the final part of the course, we will give you a flavour of important ideas in interacting topological systems, such as the fractional quantum Hall effect and the path towards topological quantum computation.