Postgraduate Research Student
Email: email@example.comRoom Number: Queens’ Building, Room: W313
William’s main research interests are in combinatorics. Most of William’s work has been on extremal problems: developing methods which show how certain properties can be extremised subject to specified structural constraints. A representative sample of such problems are Erdos-Ko-Rado type questions where we seek to maximise the size of an intersecting family of objects. Another class of extremal problems are isoperimetric inequalities where the task is to minimise the boundary of subsets of a certain space (e.g perimeter of shape in the plane, vertex boundary of subset of a graph). William is particularly fond of problems which are easily stated and understood, but which elude attack by standard arguments.
William is supervised by David Ellis and has so far worked on the following problems:
- Erdos-Ko-Rado for triangulations
- Isoperimetric inequality for r-sets
- Maximising maximal paths in the grid and cube
- Maximising codimension of covering spaces of binary words