Mathematical Sciences: Conformal Dynamical Systems and Teichmuller Theory

琳达基恩将致力于共形理论中的问题 含有附加参数的动力系统 黎曼曲面理论的问题。丽莎戈德堡也将 开展复杂动力学研究。她将调查 包括计算基本群的问题 一般有理映射的模空间的性质及 在朱莉娅集上扩展整个地图的动作。 的共轭类的一般刻画问题 整体功能是基恩研究的主要焦点。她将 主要处理函数类， 点和多个渐近值。戈德堡会试图 找到Kleinian群范畴中结果的推广， 某些亚纯函数类为了研究 这些功能的动力学，有必要研究 对应的Julia集和稳定集的几何。

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.