A Survey on Quantum Groups

In this mostly expository talk, I will motivate the study of locally compact quantum groups by investigating the compact setting. We will explore a handful of interesting examples, indicating how the ``quantization'' procedure enriches the subject and gesturing toward the nuances of the locally compact analogs. We will introduce corepresentations and discover how these primitive unitaries descend to historic relations among classical abelian groups. This last discovery is part of joint work with Huang, Krajczok, and Tobolski.