Topological Superconductivity

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"Conventional" superconductivity is one of the most dramatic phenomena in condensed matter physics, and yet by the 1970's it was fully understood - a solved problem much like quantum electrodynamics. The discovery of high temperature superconductivity changed all that and opened the door, not only to higher Tc's, but also to a wealth of even more exotic phenomena, including things like topologically ordered superconductors with factional vortices and non-Abelian statistics. I will describe some of the evolution of the field of exotic superconductivity, with a focus on recent theoretical and experimental work which sheds light on whether strontium ruthenate supports topological chiral superconductivity.