Mathematical Sciences: Geometry and Topology of Complex Variables and Manifolds in Low Dimensions

Walter Neumann将继续研究复杂曲线和曲面的拓扑结构及其奇点，特别是复杂结构的存在对相关3-和4-流形的拓扑和拓扑不变量的影响。他还将研究低维实数流形和复杂流形上的几何结构，包括奇异结构、结构的变形、它们的不变量以及与不变量相关的算术问题。几何学和代数之间的显著联系在每一个转折点都被揭示出来。

Walter Neumann will continue his study of the topology of complex curves and surfaces and their singularities, particularly the influence of the existence of complex structures on the topology and topological invariants of the associated 3- and 4- manifolds. He will also study geometric structures on real and complex manifolds in low dimensions, including singular structures, deformation of structures, their invariants, and arithmetic questions related to the invariants. Remarkable connections between geometry and algebra are uncovered at every turn.