Apparently without consulting Dr. Jacobs, Swen considers several options for Jeremy. On his own, he decides to give Jeremy the problem of synthesizing a new derivative of the complex Beverly had discovered. There are good reasons for such a convention. At a minimum, central authority and control are needed for coordinating work on a grant that supports graduate students. The research group leader or PI is usually in the best position to make good matches between students and projects.
Graduate students have much at stake in the allocation of projects.
Someone with authority should be answerable and be seen to be answerable for assigning portions of the research to students. If Dr. Jacobs makes it a practice to allow Swen or other post-docs to allocate research problems, he cannot relinquish all responsibility. There remains a need for coordination and oversight on his part to ensure that post-docs are properly trained in this task and that graduate students' interests are properly protected. Advisers have responsibility for attending to these needs as part of the duties of advising graduate students and post-docs. This kind of attention is necessary to manage funded projects well.