The asymptotic structure of Einstein's theory is particularly rich, revealing infinite-dimensional symmetry algebras. This subject will be the subject of lectures spread over several years. The 2021-2022 lecture will be devoted to asymptotically anti-de Sitter spacetimes in dimension 3, where the symmetry algebra is a direct sum of two copies of the Virasoro algebra (with traditional boundary conditions). Subsequent lectures will be devoted to asymptotically flat spacetimes, where the symmetry algebra is the infinite-dimensional Bondi-Metzner-Sachs (BMS) algebra. The lectures will be supplemented by research seminars, close to the subject of the lecture and presenting a sample of the major challenges in the field.
Questions addressed in 2021-2022:
- Hamiltonian formulation of general relativity and asymptotic symmetries
- Three-dimensional gravitation with negative cosmological constant and Chern-Simons theory
- Asymptotic conditions, Virasoro algebra and central charge
- Black holes, entropy and Cardy's formula
- Hamiltonian reduction, edge theory
- Time-dependent extensions (supergravity, high spins)
