Mathematical Sciences: Conformal Dynamical Systems and Teichmuller Theory

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Linda Keen will work on problems in the theory of conformal dynamical systems which are concerned with accesory parameter problems from Riemann surface theory. Lisa Goldberg will also carry out research in complex dynamics. She will investigate problems which include the computation of the fundamental group of the moduli space of a generic rational map and the analysis of the action of an expanding entire map on its Julia set. The general problem of characterising conjugacy classes of entire functions is the main focus of Keen's research. She will work principally with the class of functions with no critical points and finitely many asymptotic values. Goldberg will try to find extensions of results in the category of Kleinian groups to certain classes of meromorphic functions. In order to study the dynamics of these functions it is essential to investigate the geometry of the corresponding Julia sets and stable sets.