Abstract:  Quantum control of atomic states has enabled understanding and tests of
fundamental physics, produced incredibly accurate timekeeping, and
advanced quantum computation and simulation. Molecules have extra
degrees of freedom that bring both challenges and opportunities if they
can be controlled at the quantum level. Active development of molecular
control techniques has already produced impressive results. After an
overview of the state of the art with small numbers of simple molecules,
I will focus on one particular application: searches for new physics
through time-variation of fundamental constants. Some models of quantum
gravity and some classes of dark matter predict temporal changes in the
proton-to-electron mass ratio. Molecular vibrations are sensitive to
these changes. I will describe our work at Amherst with singly ionized
oxygen molecules, both in a beam and a trap, and its prospects for
testing physical laws.