Mathematical Sciences: "Ramifications of Value Distribution"

在这个项目中，首席研究员和他的学生 将致力于研究复变理论中的一些问题 以复杂函数的值的分布为中心。 特别是，他们将研究其衍生物和价值- 拟正则映射的分布性质 Gross星星定理和Plessner定理中的例外集 定理，以及Nevanlinna理论中的误差项。 在 此外，首席研究员和他的学生将 探索其中一些工作的应用， 微分方程和复迭代。 复变量理论的领域已经有了很长的时间， 杰出的历史，首席研究员是其中之一， 复变理论领域的领导者 复杂函数值的分布。 在 这个项目的主要研究者将与毕业生 学生扩展我们的知识的价值分布 各种函数类的性质， 复平面上微分方程的解。

In this project the principal investigator and his students will work on a number of problems in complex variable theory centered around the distribution of values of complex functions. In particular, they will study the ramification and value- distribution properties of quasi-regular mappings, the exceptional set in the Gross star theorem and in Plessner's theorem, and the error term in the Nevanlinna theory. In addition, the principal investigator and his students will explore the application of some of this work to problems in differential equations and complex iteration. The area of complex variable theory has had a long and distinguished history, and the principal investigator is one of the leaders in the subarea of complex variable theory concerned with the distribution of the values of complex functions. In this project the principal investigator will work with graduate students to extend our knowledge of the value-distribution properties of various classes of functions that arise as solutions of differential equations in the complex plane.