Admittedly, this is a soft question.
My own experience in mathematical research has been of long periods of research, mostly characterized in long "blocks" and sporadic breakthrough.
How does this image fit with research semesters, in which many researchers (veterans, early careers, postdocs and students) gather at a single institution, e.g., ICERM, IPAM etc., for a few months? What kind of research do one usually do in these sorts of semesters? Should one get there with a well defined project a-priori? Do you find this format effective for mathematical research?