Black holes: bridges between number theory and holographic quantum information
BLH
4 September 2023 to 20 December 2023
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Programme theme
Defining a theory of quantum gravity remains one of the most challenging problems at the cutting edge of research in mathematical and theoretical physics. Unlocking this problem implies constructing a quantum field theoretic description of gravity which fully elucidates how a quantum field theory encodes gravitational spacetime background solutions.
Much of the progress in shaping the language and the framework of this problem owes its genesis to a specific subset of problems in quantum gravity, namely those dealing with understanding the organisation of information in black holes.
These problems in turn can be neatly divided into two streams of research, each dealing with a different class of black holes as systems of interest:
- The enumeration of the quantum microstates of a special class of black holes, called BPS black holes, in superstring theories through Mock modular forms and automorphic forms. This has led to uncovering a cornucopia of exciting connections between string theory and mathematical structures in the fields of number theory, finite group theory and algebraic geometry, such as the relation of BPS black holes and Mock modular forms, the relation of Moonshine and the K3 elliptic genus, and produced significant new results in the theory of automorphic forms.
- Holographic quantum information as encoder of black hole entropy. This approach contains a dazzling array of ideas and concepts rooted in the field of quantum information theory, such as quantum error correction codes and computational complexity theory, and promisingly bold new conceptual templates such as encoding aspects of black hole thermodynamics in terms of quantum extremal surfaces.
These two parallel streams of research in quantum gravity have, in the last decade, experienced unprecedented conceptual and computational leaps, with recent work on the relation of Moonshine, conformal field theories and quantum error corrections codes, as well as attempts in defining computational complexity for black holes, strongly suggesting a powerful connection between these two streams of research into quantum gravity.
The primary objective of this programme is to synergistically bring together mathematicians, mathematical physicists, string theorists and quantum information researchers in these two parallel streams united by their common focus on understanding black hole entropy. The goal is to use powerful emerging computational tools such as machine learning, and cross-pollinating concepts and calculational toolkits across disparate research lines, in order to make decisive advances in our understanding of black holes in quantum gravity.
Week November 27-December 1, 2023: Workshop on Bridges between holographic quantum information and quantum gravity
Workshops
Number theory, machine learning and quantum black holes
2 October 2023 to 6 October 2023
Machine learning toolkits and integrability techniques in gravity
6 November 2023 to 10 November 2023
Bridges between holographic quantum information and quantum gravity
27 November 2023 to 1 December 2023
Organisers
- Alejandra Castro University of Cambridge
- Robert de Mello Koch Huzhou University
- Yang-Hui He London Institute for Mathematical Sciences; University of Oxford; City, University of London
- Gabriel Lopes Cardoso Instituto Superior Técnico, Lisboa
- Sameer Murthy King's College London
- Suresh Nampuri Instituto Superior Técnico, Lisboa
- Larus Thorlacius University of Iceland
Supported By
