### Decision problems in one-relation semigroups

## Abstract

I will give an overview and introduction to the most important decision problems in combinatorial semigroup theory, including the word problem, and describe attempts to solve a problem that has been open since 1914: the word problem in one-relation semigroups. I will link it with some of my results from formal language theory, as well as recent joint work with I. Foniqi and R. D. Gray (East Anglia) on proving undecidability of certain harder problems, proved by way of passing via one-relator groups.