Glen Hall will carry out research into problems in the theory of dynamical systems motivated by celestial mechanics. Hall will focus his attention on two problems in particular. The first is the study of exact symplectic twist diffeomorphisms of four dimensions. The goal is to give examples of pathological behavior, give regularity theorems of invariant sets and obtain a better understanding of the topology of periodic orbits. The second problem is the study of central configurations, particularly extreme cases of a few large masses and many small equal masses. The goal is to find techniques for these extreme cases which will allow extensions of these results to the n-body problem and will include analytic and numerical work.
