LivMS Popular Lecture – Duality: Where things are equal, but opposite

Duality: Where things are equal, but opposite

Dr. Rose Wagstaffe

Wednesday 21st October 2026, 5:00PM

This lecture is face-to-face on the University of Liverpool’s campus, in Lecture Theatre C of the Central Teaching Hub. This is building 221 in square F7 of https://www.liverpool.ac.uk/files/docs/maps/liverpool-university-campus-map.pdf. Please note that Eventbrite’s map is showing the wrong location.

It is suitable for anyone aged 16 or over with an interest in mathematics. Please book one ticket for each person attending. There will not be a live stream or a recording.

We are all used to things being equal. How do we understand when things are opposite? And what do we actually mean by ‘opposite’? Category Theory provides the language to understand such concepts, and we may find that two quite different-looking objects are actually equivalent – or equivalent with some twist. This concept of ‘twisted equality’ is called duality, and can be used to understand and relate very different areas of maths. I studied it during my PhD, and look forward to sharing this fascinating topic with you.

About the speaker

Dr Rose Wagstaffe is a Lecturer in Pure Mathematics at the University of Manchester. Her research explores mathematical logic, including model theory and its connections with algebra and category theory. She is passionate about sharing the beauty and breadth of mathematics with wider audiences.