The mathematics of the AdS/CFT correspondence

这个项目涉及弦理论和量子场论的数学。弦理论是一种公认的“万有理论”，对数学产生了巨大的影响。该项目的长期目标是将弦理论发展成为数学中的一门学科。更直接、更容易实现的目标是在数学上发展弦理论的一部分（由超对称保留的部分），并在这种情况下证明某些弦的对偶性。该项目侧重于AdS/CFT对应，这是理论物理中的一个主要主题（有超过10,000篇论文），但尚未用数学公式表示（除了少数特殊情况）。本课题在代数几何、几何表示理论及相关领域具有广泛的应用前景，是博士、硕士研究生的优秀课题。

This project concerns the mathematics of string theory and quantum field theory. String theory is a putative "theory of everything", which has had a huge impact on mathematics. The very long-term goal of this project is to develop string theory as a discipline within mathematics. The more immediate, and very much attainable, goals are to develop mathematically a part of string theory (the part preserved by some supersymmetry), and to prove in this context certain string dualities. The project focuses on the AdS/CFT correspondence, which is a major topic in theoretical physics (with over 10,000 papers) but which has not been formulated mathematically (except in a few special cases). This project has many potential applications in algebraic geometry, geometric representation theory and related fields, which would be excellent projects for PhD and masters students.