  These days, Franco Iachello is {\it the\/} eminent practitioner applying
classical and finite groups to physics. In this he is following a tradition at
Yale, established by the late Feza Gursey, and succeeding Gursey in the Gibbs
chair; Gursey in turn, had Pauli as a mentor. Iachello's striking achievement
has been to find an actual realization of arcane supersymmetry within mundane
adjacent even-odd nuclei. Thus far this is the only {\it physical\/} use of
supersymmetry, and its fans surely must be surprised at the venue. Here we
describe the role of $SO(2,1)$ conformal symmetry in non-relativistic
Chern--Simons theory: how it acts, how it controls the nature of solutions, how
it expands to an infinite group on the manifold of static solutions thereby
rendering the static problem completely integrable. Since Iachello has also
used the $SO(2,1)$ group in various contexts, this essay is presented to him on
the occasion of his fiftieth birthday.
