Mathematical Sciences: Chern-Weil Theory for Topological Groups

David Stone将研究几何问题，这些问题的动机来自于计算物理学。所使用的技术来自几何学和拓扑学。他将应用组合方法，在过去已经使用数值积分。Stone的研究涉及从局部几何数据中提取空间的全局拓扑信息的一般问题。在经典微分几何中，数据以无穷小的形式呈现，chen - weil理论从它们进一步构造无穷小，当积分时，产生所需的特征类。斯通将发展整个陈-韦尔理论的系统模拟，它不使用无穷小，而是使用代数拓扑技术。这项工作有望在晶格规范场的理论中有物理应用。

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.