- Assoc. Prof John Bamberg
- Assoc. Prof Gordon Royle
- Prof. Alice Niemeyer

Some problems on the existence and non-existence of ovoids and related objects in polar spaces.

My research is in exploring the structure of a class of finite geometries called polar spaces. In particular, I am investigating the existence and non-existence of objects such as m-ovoids and spreads, which are certain “maximal” configurations of points and lines. The focus of the research is on classical polar spaces and classical generalised quadrangles, which are related to projective spaces. There are a number of existence/non-existence results in the literature, but there are also many objects whose existence is not yet known. I am employing a number of theoretical and computational techniques to extend and generalise these existence results.

Research into finite geometry is important because it gives insight into their structure - structure which is often exhibited in in other situations. Thus understanding them can provide tools to help in other fields such as cryptography and coding theory.

- Australian Postgraduate Award