  We study the nonperturbative quantum evolution of the interacting O(N) vector
model at large-N, formulated on a spatial two-sphere, with time dependent
couplings which diverge at finite time. This model - the so-called "E-frame"
theory, is related via a conformal transformation to the interacting O(N) model
in three dimensional global de Sitter spacetime with time independent
couplings. We show that with a purely quartic, relevant deformation the quantum
evolution of the E-frame model is regular even when the classical theory is
rendered singular at the end of time by the diverging coupling. Time evolution
drives the E-frame theory to the large-N Wilson-Fisher fixed point when the
classical coupling diverges. We study the quantum evolution numerically for a
variety of initial conditions and demonstrate the finiteness of the energy at
the classical "end of time". With an additional (time dependent) mass
deformation, quantum backreaction lowers the mass, with a putative smooth time
evolution only possible in the limit of infinite quartic coupling. We discuss
the relevance of these results for the resolution of crunch singularities in
AdS geometries dual to E-frame theories with a classical gravity dual.
