Proving the Landau-Ginzburg/Conformal Field Theory correspondence

这个项目的目的是提供简单奇点的Landau-Ginzburg/Conform场论(LG/CFT)对应的第一个精确的数学描述和几何证明，简单奇点是一个物理激励原理，它将代数几何中的超曲面奇点与共形场论中的顶点代数表示联系起来。这里发展的形式主义有望澄清对应的性质，并直接导致超越简单奇点的概括，以及提供一本词典，将CFT的方法转换为奇点理论，反之亦然。这些成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.