The PIMS Postdoctoral Fellow Seminar: Canon Sun

The wavefunction of a particle describes everything that could be known about a quantum mechanical system. One of the key insights over the past few decades is that a wavefunction, despite its name, is not an ordinary function, but should be regarded mathematically as a section of a vector bundle. In this view, an interesting possibility opens up: the vector bundle may not be topologically trivial. To determine whether a bundle is trivial, mathematicians have devised a wide array of topological invariants, such as the Chern number, to probe its topology. Although the description of the Chern number is purely mathematical in nature, it turns out to be directly measurable in real-life, physical experiments. In this talk, I will discuss how certain topological invariants can be directly probed and measured. Specifically, I will focus on hyperbolic lattices, where there is a myriad of topological invariants one could consider.