Mathematical Sciences: Global Differential Geometry and Singularities

9628522亚当斯这笔赠款支持佐治亚大学的六名数学家，他们有着相互关联的兴趣。研究领域包括几何和拓扑学，包括Seiberg-Witten理论，奇异簇的特征类，可积系统和哈密顿动力学，以及肖特基问题。部分资助用于旅行、一个研讨会、两名博士后研究人员和几名研究生。Seiberg-Witten理论位于几何分析、拓扑学和代数几何的交界处，是理论物理中最新的发现。在这个理论中，电磁二元性起着至关重要的作用，粗略地说，电和磁是一个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.