Finite Geometry

Finite geometry is the study of geometries of systems with a finite number of points. A basic description can be found on Wikipedia's finite geometry page. See finitegeometry.org for a nice collection of links related to this dispcipline.

Publications/Presentations

John Fuelberth, Athula Gunawardena and C. David Shaffer, On incidence structures of nonsingular points and hyperbolic lines of ovoids in finite orthogonal spaces, Designs, Codes and Cryptography (2009).

Student projects

While at Penn State Behrend Michael O. McCracken completed an enumeration of classical ovoids in O6+(8) using a parallelized version of the ovoid search software written by Athula Gunawardena.

I am hoping to have a student (soon) who will resurrect Mike's work and perform an isomorphism check on the ovoids that resulted. This is no small task as I recall several million ovoids.