Inaugural Lecture -- Professor Colva Roney-Dougal Perfect symmetry: counting what matters

Before dying in a duel at the age of 20, Évariste Galois made some of the first discoveries in what came to be known as group theory: the study of symmetry. Symmetry is important right across the sciences, and this talk will start by describing what groups are, and why mathematicians find them beautiful.
Alan Turing, the World War II code-breaker and inventor of programmable computers, suggested that one use for his (then imaginary) machines might be to count groups. We have since followed up on his suggestion. This talk will give a non-technical introduction to some of the different ways we can try to count groups, and the variety of answers we find to the related question “what does a random group look like?”. We'll finish with a recent solution to a pair of 30-year-old conjectures.