The incidence graph of a generalised quadrangle is characterised by being a connected, bipartite graph with diameter four and girth eight. We can think of them as a set of points and lines without triangles (hence the name). Generalised quadrangles have their own rich theory, which dates back to the work of Tits on groups of Lie type.
In this project, we will study finite generalised quadrangles: we look for constructions, classifications and characterisations. Generalised quadrangles fall into the more general class of generalised polygons (diameter n, girth 2n). A classic theorem of Higman and Feit shows that a finite generalised polygon is either a di-gon (n=2), a projective plane (n=3), a generalised quadrangle (n=4), a generalised hexagon (n=6) or a generalised octagon (n=8). This project studies generalised quadrangles and/or polygons and can take multiple directions, according to your interests.
Supervisors
Primary Supervisor: Geertrui Van de Voorde
Key qualifications and skills
Strong background in linear algebra and (finite) fields and knowledge of basic discrete mathematics.
(If at UC: high grades in MATH203 and MATH321, and ideally in MATH220/MATH324)
Does the project come with funding
No - Student must be self-funded
Final date for receiving applications
Ongoing
How to apply
Email to primary supervisor. Include an overview of relevant courses you have taken (and the grades you obtained).
Keywords
combinatorics; finite geometry
