The Zarankiewicz problem through linear hypergraphs and designs

Zarankiewicz问题是一个著名的开放问题，与许多不同的数学领域有着深刻的联系。尽管世界上一些最著名的数学家一直在关注这个问题，但这个问题70多年来一直没有得到解决。该项目旨在通过使用一种基于组合设计理论领域的新方法，在Zarankiewicz问题上取得重大进展。这种方法将利用关于稠密超图的边分解的设计理论的最新重大突破。

The Zarankiewicz problem is a famous open problem with deep connections to many different areas of mathematics. Despite continued attention from some of the world's most celebrated mathematicians, it has remained unsolved for over 70 years. This project aims to make major progress on the Zarankiewicz problem by utilising a novel approach based in the field of combinatorial design theory. This approach will leverage recent major breakthroughs in design theory concerning edge decompositions of dense hypergraphs.