Mathematical Sciences: "Ramifications of Value Distribution"

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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.