Mathematical Sciences: Global Differential Geometry and Singularities

9628522 Adams这项资助资助了乔治亚大学一个由六名兴趣相关的数学家组成的小组。研究领域包括几何和拓扑学，包括Seiberg-Witten理论，奇异变分的特征类，可积系统和哈密顿动力学，以及肖特基问题。部分支持旅费、研讨会、两名博士后研究人员和几名研究生。Seiberg-Witten理论是几何分析、拓扑学和代数几何的交叉点；这是由理论物理问题引起的一项新发现。在这个理论中，电磁二象性起着至关重要的作用，它大致说明电和磁是单一潜在现象的两个阶段。

9628522 Adams This grant supports a group of six mathematicians at the University of Georgia with interrelated interests. Research areas lie in geometry and topology including Seiberg-Witten theory, characteristic classes of singular varieties, integrable systems and Hamiltonian dynamics, and the Schottky problem. Partial support is provided for travel, a workshop, two postdoctoral researchers, and several graduate students. Seiberg-Witten theory lies in the interface of geometric analysis, topology and algebraic geometry; it is a recent discovery motivated by problems in theoretical physics. In this theory, electric-magnetic duality plays a crucial role which states roughly that electricity and magnetism are two phases of a single underlying phenomenon.