SHULT 9701188 The principal investigator will investigate new infinite families of geometries recently discovered. Also, the PI will study locally-generated geometries generalizing some earlier results to characteristic two. This area bears some relation to the classification of the finite simple groups. Finally, the PI will look at point-line characterizations of classical geometries of infinite rank. The field of group theory is the mathematical theory of symmetry and interacts with many other disciplines, for example physics and chemistry outside of mathematics, coding theory, number theory and geometry inside mathematics. The investigator's particular area is finite groups and geometries. It is an old subject but still facing great unsolved problems and with many opportunities for breakthroughs.
