The following people are in this group:
Mr Joe Allen Mathematics (PhD) joe.allen@bristol.ac.uk
Dr Tim Burness Reader in Pure Mathematics Tel. (0117) 42 84902 t.burness@bristol.ac.uk
Professor Tim Dokchitser Heilbronn Chair in Algebraic/Arithmetic Geometry Tel. (0117) 42 84968 tim.dokchitser@bristol.ac.uk
Dr Alex Malcolm Heilbronn Research Fellow alex.malcolm@bristol.ac.uk
Dr Simon Peacock Honorary Research Fellow simon.peacock@bristol.ac.uk
Professor Jeremy Rickard Professor of Mathematics Tel. (0117) 42 84904 j.rickard@bristol.ac.uk
Representation theory, in its broadest sense, is the art of relating the symmetries of different objects.
To study symmetry in the first place, mathematicians introduced the notion of a group.
For instance a square has four bilateral symmetries (reflections across diagonals or across lines connecting opposite borders) and four rotational symmetries (by 0, 90, 180 or 270 degrees). Together these eight symmetries form a group.
Representation theory is a vast subject enjoying a close relationship with topology, geometry, number theory, combinatorics and mathematical physics.
Symmetry appears in many different guises. Galois discovered the right way to understand symmetries of a polynomial equation. For example, the equation X^4=2 has four solutions (in the complex numbers), and it turns out that there are eight symmetries of these solutions.
These symmetries form a group which has exactly the same structure as the group of symmetries of the square.