We discuss a recent line of research investigating inverse theorems with respect to general k-wise correlations, and explain how such correlations arise in different contexts in mathematics. We outline some of the results that were established and their applications in discrete mathematics and theoretical computer science. We also mention some open problems for future research.

翻译：本文探讨了近期关于一般k-wise相关性逆定理的研究脉络，并阐释了此类相关性在数学不同领域中的产生机制。我们概述了已建立的部分结果及其在离散数学与理论计算机科学中的应用，同时提出了若干有待未来研究的开放性问题。