Uploaded August 2026 | Updated September 2026, 2 weeks ago
Series Title: From Counting to Emergence in AdS/CFT
Speaker: Sanjaye Ramgoolam (Queen Mary University of London)
Abstract: Finite dimensional diagram algebras, including permutation group algebras, provide mathematical mechanisms which illuminate the counting of one-matrix and multi-matrix operators for general matrix size $N$ in the context of the AdS/CFT correspondence. Counting problems are matched with appropriate algebras. Representation-theoretic Fourier transforms on the algebras relate the diagrams to Fourier bases labelled by appropriate collections of Young diagrams. These bases have applications in the identification of giant graviton states, their open string fluctuations, their back-reacted supergravity geometries, as well as small black hole states in the dual space-time. The problem of the identification of the geometries in turn leads to new algorithms, based on graph combinatorics, for projectors in the algebras.
The sequence of three lectures will give an overview of the subject, aiming to combine a pedagogical approach building on concepts familiar from advanced undergraduate mathematical physics courses with an introduction to the key developments. Each one-hour lecture will be preceded by a 30-minute preparatory presentation pitched at a level suitable for the DIAS summer internship students. The lecture will be followed by an opportunity for questions and discussion. I also hope to present the computational and mathematical tools around counting, algebras and representation theory in a form which can be useful to post-docs working on themes related to emergence in other areas of mathematical physics.
Series Title: From Counting to Emergence in AdS/CFT
Speaker: Sanjaye Ramgoolam (Queen Mary University of London)
Abstract: Finite dimensional diagram algebras, including permutation group algebras, provide mathematical mechanisms which illuminate the counting of one-matrix and multi-matrix operators for general matrix size $N$ in the context of the AdS/CFT correspondence. Counting problems are matched with appropriate algebras. Representation-theoretic Fourier transforms on the algebras relate the diagrams to Fourier bases labelled by appropriate collections of Young diagrams. These bases have applications in the identification of giant graviton states, their open string fluctuations, their back-reacted supergravity geometries, as well as small black hole states in the dual space-time. The problem of the identification of the geometries in turn leads to new algorithms, based on graph combinatorics, for projectors in the algebras.
The sequence of three lectures will give an overview of the subject, aiming to combine a pedagogical approach building on concepts familiar from advanced undergraduate mathematical physics courses with an introduction to the key developments. Each one-hour lecture will be preceded by a 30-minute preparatory presentation pitched at a level suitable for the DIAS summer internship students. The lecture will be followed by an opportunity for questions and discussion. I also hope to present the computational and mathematical tools around counting, algebras and representation theory in a form which can be useful to post-docs working on themes related to emergence in other areas of mathematical physics.
