1. An apparatus for administering globally accessible memory space in a distributed computing system, the distributed computing system comprising a plurality of compute nodes coupled for data communications by one or more data communications networks, each compute node comprising computer memory, the apparatus comprising a computer processor, a computer memory operatively coupled to the computer processor, the computer memory having stored thereon computer program instructions that, when executed, cause the computer processor to carry out a method steps of: for each compute node: mapping a memory region of a predefined size beginning at a predefined address; executing one or more memory management operations within the memory region, including, for each memory management operation executed within the memory region: executing the operation collectively by all compute nodes, where the operation includes a specification of one or more parameters and the parameters are the same across all compute nodes; reallocating, by each compute node in a collective operation, a buffer; receiving, by each compute node from a deterministic memory management module in response to the memory management operation, a return value, where the return value is the same across all compute nodes, wherein receiving the return value from the deterministic memory management module further comprises receiving a local memory address of the reallocated buffer within the memory region, where the local memory address is the same address on all compute nodes; entering, by each compute node after local completion of the memory management operation, a barrier; and when all compute nodes have entered the barrier, resuming execution.