Topological magnons and quantum magnetism

Abstract: Investigations into the topology of band structures in solid state physics has been one of the most important conceptual and experimental enterprises in the physics of this century. In this talk I give a broad introduction to the state of the field. Then I shall focus on my own work on extending existing ideas into the realm of band structures of magnetic excitations and the connections with interesting open directions in quantum magnetism. I will say something about bulk probes of Dirac and Weyl magnons, surface probes of magnetism, the zoo of topological magnon states and the role of magnon interactions in shaping, destroying and creating nontrivial topology. I shall also connect these findings to transport and spectroscopic experiments on a variety of magnetic materials.