The Reconstruction and Recognition Problems for Hypersurface Singularities

这个项目涉及数学方面的纯基础研究。它围绕着被称为准齐次孤立超曲面奇点的几何对象和被描述为Artin Gorenstein代数的代数结构之间的令人惊讶的关系而展开。尽管国际上的专家多次试图阐明这一关系，但这种关系仍未得到充分理解。这个项目以Artin Gorenstein代数的一种新方法为武器，建议澄清这种关系的性质，并利用它来解决相关的几何和代数问题。特别是，它的目的是在经典不变量理论领域取得开创性的结果。

This project concerns pure basic research in mathematics. It is centred around a surprising relationship between geometric objects called quasi-homogeneous isolated hypersurface singularities, and algebraic structures described as Artinian Gorenstein algebras. This relationship has not been fully understood despite numerous attempts by internationally based experts to shed light on it. Armed with a novel approach to Artinian Gorenstein algebras, this project proposes to clarify the nature of this relationship and utilise it for solving related geometric and algebraic problems. In particular, it aims at obtaining a groundbreaking result in the area of classical invariant theory.