On integrable subsectors of AdS/CFT and LLM geometries

The 1/2 BPS and regular LLM geometries are formed from the backreaction of a large number of D-branes on AdS₅×S⁵.  The dual N=4 SYM operator to this configuration, and excitations thereof, thus lie outside of the planar limit of the theory.  Explicitly the operators dual to these geometries are Schur polynomials labelled by a Young diagram with O(N²) boxes and excitations of this configuration are restricted Schur polynomials obtained by adding boxes (and restriction labels) to this diagram.  A special class of these geometries are labelled by Young diagrams with O(1) well separated corners.  In the large N limit excitations localised at any one of these corners only mix with each other which is a major simplification.  A recent proposal has argued that the large N dynamics of these operators is isomorphic to that of planar N=4 SYM and thus represents an integrable subsector of N=4 SYM.  In this talk this proposal is reviewed and aspects of the weak and strong coupling evidence presented.