Mathematical Sciences: A Proposal to Settle the Jacobian Conjecture

9409775院长这个项目关注的是雅可比猜想的解。首席研究人员描述了一种新的方法来验证二维猜想。这些想法来自于关于第一Weyl代数的Jacobian猜想和Kirillov-Dixmier型猜想之间的关系的工作。文中还讨论了该方法在高维问题上的推广。众所周知，复仿射空间上的可逆多项式映射有一个非零常数的雅可比。雅可比猜想则相反：雅可比为非零常数的多项式映射是可逆的。尽管雅克比猜想在过去的五十年里吸引了大量的关注，但它在每一个维度上都是开放的。该奖项支持以一种新颖的方法来解决这个问题。

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.