Geometric Methods in Complex Analysis

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The proposal deals with geometric methods in complex analysis -- the study of functions of complex variables. Development of this field is one of the great contributions of modern mathematics. In fact, many different directions of research in modern mathematics stem from problems in complex analysis. Conversely, to study complex analysis one needs many tools from other areas - such as differential equations, topology, functional analysis, etc. In addition, complex analysis has numerous applications to other sciences. It is this inherent interconnection with other branches of mathematics, physics, and computer science that has made complex analysis one of the leading research areas in mathematics for many decades.