Monopoles, scattering, generalized symmetries

Gauge theory is a very mature subject by now. Surprisingly, some of its symmetries have only been properly understood in the last couple of years. Specifically, such theories typically have a very rich set of symmetries, involving modern notions such as higher-form symmetries, higher-group symmetries, and categorical symmetries. A proper understanding of these generalized symmetries is not really crucial if we are interested in scattering processes involving fundamental particles only, but it does become quite essential if we want to add monopoles into the mix.  In this talk I will review where these generalized symmetries come from, and how they impose
constraints on scattering amplitudes of elementary particles against heavy monopoles. This will allow us to resolve a decades-old puzzle concerning such processes, where incoming electrons appear to become fractional particles after the scattering event.