  By virtue of the Noether theorems, the vast gauge redundancy of general
relativity provides us with a rich algebra of boundary charges that generate
physical symmetries. These charges are located at codimension-2 entangling
surfaces called corners. The presence of non-trivial corner symmetries
associated with any entangling cut provides stringent constraints on the
theory's mathematical structure and a guide through quantization. This report
reviews new and recent results for non-perturbative quantum gravity, which are
natural consequences of this structure. First, we establish that the corner
symmetry derived from the gauge principle encodes quantum entanglement across
internal boundaries. We also explain how the quantum representation of the
corner symmetry algebra provides us with a notion of quantum geometry. We then
focus our discussion on the first-order formulation of gravity and show how
many results obtained in the continuum connect naturally with previous results
in loop quantum gravity. In particular, we show that it is possible to get,
purely from quantization and without discretization, an area operator with
discrete spectrum, which is covariant under local Lorentz symmetry. We
emphasize that while loop gravity correctly captures some of the gravitational
quantum numbers, it does not capture all of them, which points towards
important directions for future developments. Finally, we discuss the
understanding of the gravitational dynamics along null surfaces as a
conservation of symmetry charges associated with a Carrollian fluid.

High Energy Physics - Theory;General Relativity and Quantum Cosmology