Join us for this public lecture at UNSW, presented by Professor Martin Bridson (University of Oxford). All welcome! This event is part of the AustMS 2022 Conference.
If you ask, “how many...”, the answer should be a number. If you ask “what sort of symmetry...” the answer should be a group. Groups are the mathematical objects that describe symmetry wherever it is found, and often provide a bridge to pass from one context to another. In this talk, they will appear as we pass from the problem of deciding when two knotted pieces of string are the same to the problem of listing all finite-volume models of space and space-time. Along the way, we will consider what it means for a problem to be “hard” or even “unsolvable”, as we roam through flat earths and curved universes.
Charles Dodgson (better known as Lewis Carroll) used the word “knot” to describe any tricky puzzle. He would appreciate this landmark in our discussion: If a knot is not the not-knot, then the group of the knot is not the not-knot group. This was once a theorem of Max Dehn, now it is not; nevertheless, it is true.
Martin Bridson comes from the Isle of Man and is the Whitehead Professor of Pure Mathematics at Oxford, the President of the Clay Mathematics Institute and a Fellow of the Royal Society. His research concerns the interactions of symmetry, geometry, topology and decidability. He is a recipient of the 2020 Steele Prize for Mathematical Exposition from the American Mathematical Society.
Registration is not necessary for this event.
