The mathematics of the AdS/CFT correspondence

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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.