Geometry of Characteristic Classes

9704413麦克劳克林这个项目涉及特征类在代数几何、共形场理论和几何朗兰兹对应问题中的应用。重点是寻找非对易符号的显式公式，它将二维情形的久保田公式推广到n维一般线性群。这一推广背后的思想是，久保田公式可以从第二个陈氏类几何推导出来。特征类是‘不变’的代数对象，通常用于对空间和流形进行分类或表示某些‘拓扑’障碍。其思想是将空间所拥有的基本信息编码到代数对象中，这些对象在空间的合理变换下是不变的。然后它们提供了一个有用的计算工具，因为代数对象通常是离散的和/或有限的，而所考虑的空间几乎总是无限的。

9704413 McLaughlin This project concerns applications of characteristic classes to problems in algebraic geometry, conformal field theory, and the geometric Langlands correspondence. An emphasis is to be placed on finding explicit formulae for non-commutative symbols which generalize to the n-dimensional general linear group a formula of Kubota for the two-dimensional case. The idea behind this generalization is that Kubota's formula can be derived geometrically from the second Chern class. Characteristic classes are 'invariant' algebraic objects often used to classify spaces and manifolds or indicate certain 'topological' obstructions. The idea is to encode essential information possessed by a space in algebraic objects that are unchanged under reasonable transformations of the space. They then provide a useful computational tool since algebraic objects often are discrete and/or finite whereas the space under consideration is almost always infinite.