Mathematical Sciences: Problems in Function Theory, Partial Differential Equations and Holomorphic Dynamics

在这个项目中，主要研究人员将致力于函数论、偏微分方程和拟共形映射中的一些问题。特别是，Eremenko教授将继续他在全纯动力学问题上的工作，特别是复迭代理论。他还将研究整函数、亚纯函数和次调和函数的理论。刘易斯教授将继续他在抛物型偏微分方程和对称定理方面的工作。最后，关于Littlewood猜想的联合工作计划涉及到整个函数。偏微分方程式和复变函数论这两个经典领域有许多共同之处，从这两个角度看问题所获得的见解往往特别具有启发性。在这个项目中，主要研究人员将单独和共同研究复映射、抛物型偏微分方程和全纯动力学中各种相互关联的问题。

In this project the principal investigators will work on a number of problems in function theory, partial differential equations and quasiconformal mappings. In particular, Professor Eremenko will continue his work on problems in holomorphic dynamics, specifically complex iteration theory. He will also work on the theory of entire, meromorphic and subharmonic functions. Professor Lewis will continue his work on parabolic partial differential equations and symmetry theorems. There is finally joint work planned on a conjecture of Littlewood involving entire functions. The classical fields of partial differential equations and complex function theory have a great deal of material in common, and very often the insights gained from viewing a problem from both viewpoints can be especially illuminating. In this project the principal investigators will work individually and jointly on various interrelated problems in complex mappings, parabolic partial differential equations and holomorphic dynamics.