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

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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.