Proving the Landau-Ginzburg/Conformal Field Theory correspondence

该项目旨在为简单奇点的朗道-金兹堡/共形场论（LG/CFT）对应关系提供第一个精确的数学陈述和几何证明，这是一个物理动机原理，将代数几何中的超曲面奇点与共形场论中顶点代数的表示联系起来。这里发展的形式主义有望澄清对应的本质，并直接导致超越简单奇点的推广，以及提供将CFT方法转换为奇点理论的字典，反之亦然。这些结果将进一步巩固澳大利亚在纯数学和数学物理研究方面的国际领先地位。

This project aims to provide the first precise mathematical statement and geometric proof of the Landau-Ginzburg/Conformal Field Theory (LG/CFT) correspondence for simple singularities, a physically motivated principle that relates hypersurface singularities in algebraic geometry to representations of vertex algebras in conformal field theory. The formalism developed here is expected to clarify the nature of the correspondence and lead directly to generalisations beyond simple singularities, as well as provide a dictionary to translate methods of CFT into singularity theory and vice versa. These results will further cement Australia's reputation as an international leader in pure mathematics and mathematical physics research.