A summary of recent results on 1-relator groups (Jack Button, NBSAN Essex, 10th July 2015)

Abstract: The study of 1-relator groups, namely groups defined by a finite presentation having a single relator, goes back at least as far as the work of Magnus in the 1930s. We consider some questions and results about this seemingly tractable but sometimes surprising class of groups, including progress from the last few years.