Mathematical Sciences: Cohomological Problems in Differential Equations and Mathematical Physics

伊恩安德森将继续他的调查 变分双复形这是一个迅速发展的话题 进入变分法研究的前沿 它的应用范围从部分守恒定律 微分方程的黎曼结构和变分 微分几何中的问题 变分双复形是微分双复形 它的名字来源于一个事实， 微分可以用欧拉-拉格朗日算子来表示 从变分法中。安德森的工作将集中在 主要是对上同调的计算 变分双复形当应用于微分系统时， 这个上同调的重要性来自于以下事实： 它的产生，部分是由守恒定律的， 方程在这种情况下，安德森将调查案件的 超定方程组纤维上的群作用 丛也引起了计算等变的问题 上同调这里安德森将进行计算， 数学物理感兴趣的案例。

Ian Anderson will continue his investigations of the variational bicomplex. This is a topic which has rapidly moved into the forefront of research into the calculus of variations. Its applications range from conservation laws of partial differential equations to Riemannian structures and variational problems in differential geometry. The variational bicomplex is a bicomplex of differential forms which derives its name from the fact that one of its differentials may be identified with the Euler-Lagrange operator from the calculus of variations. Anderson's work will focus principally on the calculation of the cohomology of the variational bicomplex. When applied to systems of differential equations the importance of this cohomology arises from the fact that it is generated, in part, by the conservation laws of the equations. In this context Anderson will investigate the case of over-determined systems of equations. Group actions on a fiber bundle also give rise to the problem of calculating equivariant cohomology. Here Anderson will carry out the computations in cases of interest to mathematical physics.