Shangshun Zhang (U. Minnesota) Ground state and low-energy excitations of a quantum critical superconductor At a quantum critical point of a metal, the critical order parameter fluctuations become soft and mediate singular interactions between electrons. For a large class of models, quantum-critical physics at low energies is described by an effective 0+1 dimensional model with an effective frequency-dependent interaction V (Omega) ~1/Omega^gamma. The value of gamma is determined by a specific microscopic model. This singular interaction gives rise to two competing tendencies towards either a non-Fermi liquid normal state or a superconducting state. In this talk, I show that the pairing of electrons wins the competition. The gap function strongly depends on frequency and possesses an array of dynamical vortices in the complex frequency plane. The vortices enter the upper half-plane one by one upon increasing gamma, and each new vortex gives rise to an additional peak in the density of states. We show that the low-energy excitations above the superconducting ground state display a traditional BCS-like behavior at gamma<1/2 but deviate from BCS behavior at gamma>1/2. These deviations lead to measurable features in the density of states and in the spectral function.