The study of hyperbolic 3-manifolds has made tremendous progress in the past five years. The new tools available have great potential for attacking previously inapproachable questions. These new tools include Perelman's Ricci flow techniques, the presently quite sophisticated theory of discrete subgroups of PSL(2,C), and interactions with number theory via arithmetic lattices. Peter Storm will work to apply these new tools to the study of 3-manifolds, and more general negatively curved spaces such as Gromov hyperbolic spaces, or higher dimensional negatively curved manifolds.
A 3-manifold is a mathematical object which models the three dimensional world we occupy. Thus questions about the nature of 3-dimensional space become mathematical questions about 3-manifolds. For this and other reasons, 3-manifolds are carefully studied by many mathematicians. They occupy a special niche between strongly intuitive subjects, such as geometry in the plane, and more abstract subjects, such as the study of mathematical objects with more than 4 dimensions, where meaningful mental images are difficult to produce. The research of Peter Storm tries to benefit from both the intuitive and the more abstract points of view, with the goal of gaining a better understanding the nature of three dimensional objects, and their mathematical cousins.
