1. A method of endpoint-based parallel data processing with non-blocking collective instructions in a parallel active messaging interface (‘PAMI’) of a parallel computer, the parallel computer comprising a plurality of compute nodes that execute a parallel application, the PAMI comprising data communications endpoints, each endpoint comprising a specification of data communications parameters for a thread of execution on a compute node, including specifications of a client, a context, and a task, the endpoints coupled for data communications through the PAMI, the method comprising: establishing by the parallel application a data communications geometry, the geometry specifying, for tasks representing processes of execution of the parallel application, a set of endpoints that are used in collective operations of the PAMI, including associating with the geometry a list of collective algorithms valid for use with the endpoints of the geometry; registering, by the application in each endpoint in the geometry, a dispatch callback function for a collective operation; and executing, by the application without blocking, through a single one of the endpoints in the geometry, an instruction for the collective operation, the instruction specifying communications of transfer data among the endpoints of the geometry, an identifier of the dispatch callback function associated with the collective operation, and a collective algorithm.