Unraveling the Relationship between Topology and Physics (Prof. Max Lein, AIMR-Tohoku University)

Unraveling the Relationship between Topology and Physics 

The theoretical explanation of the Quantum Hall Effect by Thouless, Kohmoto, den Nijs and Nightingale as well as Hatsugai linked an abstract mathematical quantity, the Chern number, to a physically measurable quantity, the transverse conductivity. This gave rise to the field of topological insulators, and since then topological effects have been realized not just in quantum systems but also for e. g. mechancial and electromagnetic waves in a number of spectacular experiments, and researchers have discovered a lot of beautiful new physics and mathematics. Unfortunately nowadays the moniker “topological” is attached to many physical effects, even though often the precise nature of the link to topology is obscure. In this talk, I will critically explore what “topological” means using examples from a wide variety of physical systems, and investigate ways in which “topology” is helpful to understand physical phenomena. I will also discuss situations where phenomena are actually not topological even though at first glance they may seem to.