Mathematical Sciences: Chern-Weil Theory for Topological Groups

大卫斯通将致力于几何问题，其动机 来自计算物理学。要使用的技术来自 从几何学和拓扑学上。他将运用组合 过去一直使用数值积分的方法。 斯通的研究关注的是提取 空间的全局拓扑信息 数据在经典微分几何中， 在无穷小的形式，和陈-韦尔理论构造从 他们进一步的无穷小，当整合，产生 所需的特征类。斯通将开发一个系统的 类似于整个Chern-Weil理论， 无穷小，但采用代数拓扑技术。这 这项工作有望在理论上得到实际应用， 格点规范场

David Stone will work on geometric problems whose motivation comes from computational physics. The techniques to be used come from geometry and topology. He will be applying combinatorial methods where numerical integration has been used in the past. Stone's research concerns the general problem of extracting global topological information about a space from local geometric data. In classical differential geometry the data are presented in infinitesimal form, and the Chern-Weil theory constructs from them further infinitesimals which, when integrated, yield the desired characteristic classes. Stone will develop a systematic analogue of the entire Chern-Weil theory that does not use infinitesimals but employs techniques of algebraic topology. This work promises to have physical applications in the theory of lattice gauge fields.