Mathematical Sciences: A Proposal to Settle the Jacobian Conjecture

[409775] Dean这个课题是关于雅可比猜想的一个解。首席研究员描述了一种在二维空间验证猜想的新方法。这些思想源于对第一Weyl代数的雅可比猜想和Kirillov-Dixmier猜想之间关系的研究。本文还讨论了将这种方法扩展到更高维度的方法。众所周知，复仿射空间上的可逆多项式映射具有一个非零常数雅可比矩阵。雅可比猜想证明了它的逆命题：具有非零常数雅可比矩阵的多项式映射是可逆的。尽管在过去的五十年中引起了大量的关注，雅可比猜想在大于1的每一个维度上仍然是开放的。这个奖项支持研究解决这个问题的新方法。

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.