. . . To encourage the growth of any science, the best thing we can do is to meet together in its interest, to discuss its problems, to criticize each other's work and, best of all, to provide means by which the better portion of it may be made known to the world. . . .
In this colloquium, I will review recent progress in understanding the claim that strongly correlated systems such as quark matter are really problems in classical gravity with an extra dimension. In the context of condensed matter, I will show that gravity duals can be tailored to model some aspects of high-temperature
superconductors. A key result is the emergence of Mott physics when an unusual scaling relationship obtains, namely discrete scale invariance. The ramifications of this much weaker form of scale-invariance symmetry, associated with log-periodic corrections to scaling, a common feature of hierarchical systems such as earthquakes and turbulence, will be explored.