I will describe how to consider the flat space limit of scaterig in AdS relative to a point (where sacttering occurs). The kinematics is related to the Wigner-Inonu contraction. In particular, I will discuss how to take the proper limits of wave functions in AdS (times extra dimensions) to understand a notion of in states and out states and how a scattering amplitude should be conceived. This will make use of the embedding formalism, where the description of these wave functions is simple. I will show how these wave functions are related to other constructions in AdS/CFT and suggest how the Mellin parameters of these other setups arise from integral representations of the wave functions in terms of Schwinger parameters.

I will discuss a novel construction of field theories based on the idea that one has only a half boson degree of freedom per lattice site. Basically, instead of having a pair of canonical conjugate commuting variables at each site, one has only one degree of freedom and the non-trivial commutators arise from connections to the nearest neighbors. The construction is very similar to staggered fermions and naturally produces gapless systems with interesting topological properties. When considering gauging discrete translations on the phase space in one dimensional examples, one gets interesting critical spin chains, examples of which include the critical Ising model in a transverse magnetic field and the 3-state Potts model at criticality. I will explain how these staggered boson variables are very natural for describing non-invertible symmetries. These non-invertible symmetries are useful to describe the critical properties of these non-trivial spin chains. Models in higher dimensions obtained this way can automatically produce dynamical systems of gapless fractons.

I will describe simple models of holography that can display some of the thermodynamics associated to small black holes. These phenomena include negative specific heat and localization on additional dimensions of the geometry. I will also explain how the dynamics of these states should naturally be thought of as partial deconfinement on a submatrix set of degrees of freedom of the model.

Half BPS states (operators) in N=4 SYM are famously described by free fermions both at weak and strong coupling. I describe a set of conjectures for a preferred class of states in more general conformal field theories that can be tested in supergravity for when such a free fermion description might arise and some motivation for it applying generally. The states in question belong to the chiral ring of a supersymmetric conformal field theory that extremize an additional U(1) charge for fixed dimension and can be reduced to multi-traces of a composite matrix field, which is equivalent to using Young tableaux (Schur polynomials) as a basis. The main conjecture asserts that if the Young tableaux are orthogonal, then the set of extremal three point functions of traces to order 1/N are determined up to a single constant. The conjecture is extended further by providing an exact norm for the Schur basis and this norm arises from a set of free fermions for a generalized oscillator algebra.

Half BPS states (operators) in N=4 SYM are famously described by free fermions both at weak and strong coupling. I describe a set of conjectures for a preferred class of states in more general conformal field theories that can be tested in supergravity for when such a free fermion description might arise and some motivation for it applying generally. The states in question belong to the chiral ring of a supersymmetric conformal field theory that extremize an additional U(1) charge for fixed dimension and can be reduced to multi-traces of a composite matrix field, which is equivalent to using Young tableaux (Schur polynomials) as a basis. The main conjecture asserts that if the Young tableaux are orthogonal, then the set of extremal three point functions of traces to order 1/N are determined up to a single constant. The conjecture is extended further by providing an exact norm for the Schur basis and this norm arises from a set of free fermions for a generalized oscillator algebra.

I will talk about a new method of performing a strong coupling expansion for many superconformal field theories in four dimensions, in particular those that are relavant for the AdS/CFT correspondence. I will first explain the methods for the case of N=4 SYM, as well as what calculations can be done (both analytically and numerically) and I will show how they compare with the dual AdS geometry. I will then explain what generalizations are required for other setups and what new field theory calculations can be done with these methods that were not available before.