Mathematical Sciences: A Proposal to Settle the Jacobian Conjecture

小行星9409775 这个项目是关于雅可比猜想的解决方案。 主要研究者描述了一种新的方法来验证二维猜想。 这些思想源于对第一Weyl代数的Jacobian猜想和Kirillov-Dixloven猜想之间关系的研究。 这种方法的扩展到更高的维度也进行了讨论。 众所周知，复仿射空间上的可逆多项式映射具有非零常数的雅可比矩阵。 雅可比猜想断言匡威：一个多项式映射的雅可比是一个非零常数是可逆的。 尽管在过去的50年里吸引了大量的注意力，雅可比猜想在大于1的每一个维度上都是开放的。 该奖项支持针对这一问题的新方法的工作。

9409775 Dean This project is concerned with a solution of the Jacobian Conjecture. The principal investigator describes a new approach for verying the conjecture in dimension two. The ideas eminate from work on the relationship between the Jacobian Conjecture and the Kirillov-Dixmier Conjecture for the first Weyl algebra. An extension of this approach to higher dimensions is also discussed. It is well known that an invertible polynomial map on a complex affine space has a jacobian which is a nonzero constant. The Jacobian Conjecture asserts the converse: a polynomial map with a jacobian which is a nonzero constant is invertible. In spite of the vast amount of attention which it has attracted over the last fifty years, the Jacobian Conjecture remains open in every dimension greater than one. This award supports work on a novel approach to this problem.