Singular spaces in analysis and geometry

奇点自然出现在数学的许多领域，作为对称、退化和渐近坍缩的模型。这个项目的目的是提供强大的，可推广的工具来阐明奇点形成模式和几何分析中出现的重要微分方程的解之间的相互作用。提出的框架建立在微局部分析的成功基础上，微局部分析是由Melrose在20世纪80年代发起的，它将Atiyah-Singer指数定理等标志性定理推广到更一般的黎曼流形上。该项目将通过提高澳大利亚在这一高度活跃的研究领域的纯数学能力而使澳大利亚受益。

Singularities arise naturally in many areas of mathematics, as models of symmetry, degeneracy, and asymptotic collapse. The aim of this project is to provide powerful, generlisable tools to elucidate the interplay between modes of singularity formation and solutions to the important differential equations which arise in geometric analysis. The proposed framework builds upon the established success of microlocal analysis, initiated by Melrose in the 1980's, in the generalisation of landmark theorems like the Atiyah-Singer index theorem to more general Riemannian manifolds. This project will benefit Australia by increasing its capacity in pure mathematics in this highly active research area.