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”，它对数学产生了巨大的影响。 这个项目的长期目标是将弦理论发展为数学中的一门学科。更直接、也更容易实现的目标是在数学上发展弦理论的一部分（由某种超对称性所保持的部分），并在此背景下证明某些弦对偶性。 该项目的重点是AdS/CFT对应，这是理论物理学的一个主要课题（有超过10，000篇论文），但还没有数学公式（除了少数特殊情况）。本课题在代数几何、几何表示理论等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.