Title. Extending partial projective planes
Speaker. J. B. Nation
Insitution. Department of Mathematics, University of Hawai’i, Honolulu
Abstract. This note discusses a computational method for constructing finite projective planes.
There are a number of interesting problems concerning finite non-desarguean projective planes. One would hope that these problems would admit an algebraic, or geometric, or combinatorial solution. But it may just be that the existence, or non-existence, of certain types of planes is an accident of nature. With that in mind, since 1999 the author has been trying various computer programs to construct non-desarguean projective planes. While all these attempts have failed, hope springs eternal, and this note describes a set of problems and some ideas for addressing them.
This note is based on a talk given to the Courant Institute geometry seminar in October 2017. The author appreciates the hospitality and encouragement from the participants of the seminar.