On the Realizability of Projective Configurations (thesis)

Abstract

Many natural questions emerge from the work of this thesis. The first chapter may inspire a budding mathematician to work (in the fashion of my thesis advisor) on area relations and equidissections. From the second chapter, one may wonder if a group of projective transformations exists over skew fields (or rings!) and if so, how to describe such an object. The third chapter bears the question of whether or not all combinatorially degenerate realizations of projective configurations hold over every projective plane. One may expand upon the fourth chapter and outline a technique for encoding any polynomial equation over F into a projective configuration. Finally, I hope that the fifth chapter compels future researches to infuse machinery from other disciplines into their studies. In addition to these listed above, Garst's thesis poses many open questions at its completion [7]. [From concluding section]