Mathematical Sciences: Differential Geometry

首席调查员将研究一些关于曲面到紧致流形的映射的问题。所考虑的映射将满足椭圆型偏微分方程式。特别是，他计划研究两个球面到齐次Kaehler流形的调和映射的模空间结构。他还将研究复射影平面中的极小曲面，并研究伪全纯曲线，以期在辛几何和其他几何中得到应用。乔恩·沃尔夫森在调和映射理论方面确立了自己的世界领袖地位。他积累了大量的技术，如半单李群的结构，复杂的代数几何和偏微分方程。调和映射的主题最近在其模空间上发现了有趣的整体结构定理后获得了突出的地位。此外，与低维拓扑中的极小表面理论和数学物理中的西格玛模型的联系导致了这一领域的研究人员数量的惊人增长。

The Principal Investigator will study a number of questions concerning maps of surfaces into a compact manifold. The maps under consideration will satisfy an elliptic partial differential equation. In particular he plans to study the structure of the moduli space of harmonic maps of the two-sphere into a homogeneous Kaehler manifold. He will also investigate minimal surfaces in the complex projective plane and study pseudo holomorphic curves with a view to applications in symplectic and other geometries. Jon Wolfson has established himself as one of the world leaders in the theory of harmonic maps. He has accumulated a vast repertory of techniques, such as the structure of semi-simple Lie groups, complex algebraic geometry and partial differential equations. The subject of harmonic maps has recently acquired prominence following the discovery of interesting global structure theorems on their moduli spaces. In addition the connections with minimal surface theory in low dimensional topology and with sigma-models in mathematical physics have led to a spectacular growth in the number of researchers in this area.