  I collect here some ideas on four topics which have not gained much
acceptance in the community. Hence, i call them conjectures. The first three of
these are in my area of expertise, and I personally consider them to be
verified, if by evidence some others might find less than convincing. On the
the fourth I do not claim expert knowledge but it has not been refuted in any
way that I understand. The first is the proposition that the ground state of a
solid made up of simple bosons is phase coherent and sustains overlap currents.
The second proposes that the cuprate superconductors upper phase transition is
into an Ong vortex liquid phase which quantizes flux and consequently exhibits
a characteristic singular, nonlinear diamagnetic behavior. The third proposes
that the metallic phase of the doped Mott insulator, if it has a Fermi surface,
has deep entanglement and an orthogonality catastrophe causing a Fermi surface
singularity. This manifests itself as the strange metal of the cuprate phase
diagram. The fourth conjecture is that the dark energy in cosmology models is
the consequence at least in part of gravitational radiation carrying energy
past us.
