Mathematical Sciences: Group Theoretic Aspects of Harmonic Maps

研究了从紧黎曼曲面到紧李群的调和映射空间的全局性质。该方法利用环群作为调和映射方程的对称群，将问题简化为考虑全纯映射的关联空间。利用构形空间理论的思想研究了从2球到各种复流形的全纯映射空间的拓扑结构，利用可积系统理论的方法研究了从2环面到紧李群的调和映射空间。

Global properties of the space of harmonic maps from certain compact Riemann surfaces to compact Lie groups will be investigated. The method uses loop groups as symmetry groups of the harmonic map equation, to reduce the problem to consideration of an associated space of holomorphic maps. The topology of spaces of holomorphic maps from the 2-sphere to various complex manifolds will be studied by using ideas from configuration space theory, and the space of harmonic maps from a 2-torus to a compact Lie group will be studied by using methods of the theory of integrable systems.