  Rogue waves in the nonlocal PT-symmetric nonlinear Schrodinger (NLS) equation
are studied by Darboux transformation. Three types of rogue waves are derived,
and their explicit expressions in terms of Schur polynomials are presented.
These rogue waves show a much wider variety than those in the local NLS
equation. For instance, the polynomial degrees of their denominators can be not
only $n(n+1)$, but also $n(n-1)+1$ and $n^2$, where $n$ is an arbitrary
positive integer. Dynamics of these rogue waves is also examined. It is shown
that these rogue waves can be bounded for all space and time, or develop
collapsing singularities, depending on their types as well as values of their
free parameters. In addition, the solution dynamics exhibits rich patterns,
most of which have no counterparts in the local NLS equation.
