Problems in Potential Theory and Dynamics in Several Complex Variables

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This project deals with questions from pluri-potentialtheory and dynamics in several complex variables. Pluri-potential theory is the higher dimensional versionof potential theory in the complex plane. The investigator plans to study certain classes of pluricomplex Green functions for the complex Monge-Ampere operator, from the point of view of theirfoliation structure and also in relation to some questionsfrom algebraic geometry. A second goal of the project is to consider polynomial estimates of Bernstein-Walsh typerelated to graphs of entire transcendental functions.The investigator plans to study certain properties ofentire functions from this point of view. Such propertiesare also of interest in transcendental number theory.Finally, the investigator is concerned with studying thedynamics of classes of polynomial automorphisms inhigher dimensions.Complex analysis in one and in higher dimensions hasimportant connections with many fields of pure and appliedmathematics and, indeed, with other sciences. It is oftenthe case that one gains insight about concrete problems once they are formulated in the context of complex numbers.This is because of the powerful methods and tools developedin the study of holomorphic functions in complex analysis.Studying complex dynamical systems proved to be importantfor understanding the behavior of more complicated real dynamical systems arising in mathematics as well as in physics and biology.