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.
