I consider myself a combinatorialist, specializing in finite geometries. Most of my work has dealt with constructing various geometrical structures or configurations, and then analyzing or characterizing those structures. The general geometric setting is typically some projective or affine space (or perhaps a circle geometry of some type) over a finite field. Some of my work on caps , point sets in some finite projective space with no three points collinear, has application to coding theory. Techniques used are typically a blend of finite field theory, elementary number theory, and finite group theory together with the usual counting arguments. In recent years I have been using various software packages, such as Magma, to help construct relatively 'large' examples and to analyze those examples in the hope of recognizing patterns that can be generalized and eventually proven as theorems. Thus I use the computer in the discovery process as opposed to using the machine as a 'number-cruncher.'

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Last modified February 2, 1998 by Gary Ebert