Second order thermal phase transitions are driven my an order parameter which comes with an amplitude. Fluctuations of this amplitude lead to a slowly decaying mode whose gap closes to zero at the critical point. I will use holographic techniques to discuss in detail how this gapped mode determines the linear response of scalar operators close to the phase transition and give a geometric expression for the dissipative coefficient that fixes the relevant Green’s functions.

Certain materials, such as the cuprate superconductors and heavy fermion materials exhibit fascinating, yet hard to explain transport properties. Holography provides a consistent framework to examine linear response and in particular transport of strongly coupled matter. I will discuss momentum dissipation in holography and show that DC transport is fixed via a Stokes flow of an "auxiliary fluid" residing on the horizon of black holes.

Condensed matter systems at quantum critical points can be described by strongly coupled field theories exhibiting anisotropic scale invariance. Lifshitz geometries been proposed to be holographic duals to these theories. I will discuss top down constructions of Lifshitz geometries in Type IIB and D=11 dimensional supergravities.

We will discuss the properties of geometries dual to BPS states of N=4 supersymmetric Yang-Mills theory. Despite the non-linearity of the problem, we develop a universal bubbling AdS description of these geometries by focusing on the boundary conditions which ensure their regularity. In the 1/8 BPS case, we find that the S3 cycle shrinks to zero size on a five-dimensional locus inside the six-dimensional base. Enforcing regularity of the full solution requires that the interior of a smooth, generally disconnected five-dimensional surface be removed from the base. The AdS5 x S5 ground state corresponds to excising the interior of an S5, while the 1/8 BPS excitations correspond to deformations (including topology change) of the S5 and/or the excision of additional droplets from the base.