Mathematical Sciences: Presidential Young Investigator

柯蒂斯·麦克马伦将继续他在动力系统理论及其拓扑分支方面的研究。其中一些工作与牛顿求方程根的算法和低次多项式的可解性有关。麦克马伦将研究函数域上的莫德尔猜想的几何图景，以及它与全纯运动、水平全纯叶层和小林度规的关系。在复杂动力学领域，他将研究Kleian群的Julia集和极限集。他还将继续他在拓扑学和方程的可解性方面的工作。

Curtis McMullen will continue his research in dynamical systems theory and its topological ramifications. Some of this work is related to Newton's algorithm for finding roots of equations and to the solvability of polynomials of low degree. McMullen will investigate a geometric picture of the Mordell conjecture over function fields and its relation to holomorphic motions, horizontally holomorphic foliations and the Kobayashi metric. In the realm of complex dynamics he will study Julia sets and limit sets of Kleinian groups. He will also continue his work in topology and solvability of equations.