Speaker
Description
In this talk, I will explain our study of the systematic expansion of $AdS_3$ Chern-Simons gravity in powers of the cosmological constant, with a focus on black hole thermodynamics. The bulk expansion generates an infinite tower of three-dimensional gravity theories invariant under successive extensions of Poincare symmetry, and we derive consistent boundary conditions and conserved charges at each order. On the boundary, the corresponding post-Carrollian expansion of the dual field theory is governed by conformal extensions of Carroll symmetry, obtained from contracting the two-dimensional conformal algebra. The black hole entropy interpolates order by order between the Virasoro Cardy formula and its $BMS_3$ counterpart, with each correction carrying a precise microscopic interpretation in the boundary theory. The exact matching between bulk thermodynamics and boundary state counting at every order reveals that the transition from $AdS/CFT$ to flat space holography has a controlled perturbative structure, and that Carrollian symmetry and its extensions emerge as the natural organizing principle.