This week

Symmetry plays an important role in quantum systems: it can constrain the dynamics, give rise to selection rules, and provide computation methods in quantum computers. In recent years there are also new types of symmetries called generalized symmetries discovered in many quantum systems, including non-invertible symmetry and higher group symmetry. These lectures will be about symmetries in various quantum systems and their applications such as constraints on the low energy dynamics. Examples will be discussed in the lectures include quantum mechanics systems, gauge theories, lattice models, and the symmetry includes ordinary and higher form symmetry as well non-invertible symmetry.

Carrollian holography suggests that gravity in four-dimensional (4d) asymptotically flat spacetime is dual to a three-dimensional (3d) Carrollian CFT living at null infinity. In this talk, I will review this framework and explain how massless scattering amplitudes in flat space can be recast as Carrollian CFT correlators at null infinity, referred to as Carrollian amplitudes. I will show that these correlators arise naturally from the Carrollian limit of holographic CFT correlators computed via AdS Witten diagrams, establishing a correspondence between the flat-space limit in the bulk and the Carrollian limit at the boundary. As a concrete application, I will briefly discuss the flat-space/Carrollian limit of the duality between 11d supergravity on AdS_4xS^7 and the 3d ABJM theory. Based on arXiv:2312.10138, arXiv:2406.19343 and work in progress.

Free strings on backgrounds such as AdS3xS3xT4 and AdS3xS3xS3xS1 can be described by integrable sigma models, which admit a very rich landscape of integrable deformations. In this talk I will focus on TsT, trigonometric and elliptic deformations which preserve some amount of supersymmetries and interpolate between well-known integrable setups. I will present the deformed geometry and check that the S-matrix encoding the scattering of excitations on the string worldsheet is compatible with factorisation.