Geometric Methods in Complex Analysis

该提案涉及复分析中的几何方法——复变量函数的研究。这一领域的发展是现代数学的伟大贡献之一。事实上，现代数学中许多不同的研究方向都源于复杂分析中的问题。相反，研究复杂分析需要许多其他领域的工具，如微分方程、拓扑、泛函分析等。此外，复杂分析在其他科学中也有许多应用。正是这种与数学、物理和计算机科学的其他分支的内在联系，使复杂分析成为几十年来数学的主要研究领域之一。

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.