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Rogue waves in the nonlocal PT-symmetric nonlinear Schrodinger (NLS) equationare 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 NLSequation. For instance, the polynomial degrees of their denominators can be notonly $n(n+1)$, but also $n(n-1)+1$ and $n^2$, where $n$ is an arbitrarypositive integer. Dynamics of these rogue waves is also examined. It is shownthat these rogue waves can be bounded for all space and time, or developcollapsing singularities, depending on their types as well as values of theirfree parameters. In addition, the solution dynamics exhibits rich patterns,most of which have no counterparts in the local NLS equation.

General rogue waves in the nonlocal PT-symmetric nonlinear Schrodinger equation