I'm back now, but this beach house in Barbados was my home for the last week, as I attended the 29th Bellairs Winter Workshop on Computational Geometry (my first time there).
The format of the workshop is very much aimed at making new research, not just sharing what the participants have done elsewhere (as many other workshops and conferences do). We met as a group twice each day for three-hour group sessions, one in the morning and another in the evening, with afternoons as free time. The sessions were held outdoors at a set of picnic tables, and participants organized themselves into smaller groups of from two or three to half a dozen or so people, to discuss different open problems that had been prepared in advance (most of which saw significant progress by the end of the workshop). Preliminary results were announced to the whole group at most sessions, so even if you worked on a subset of the problems you had a sense of what everyone else was doing. And moving from one group to another was encouraged: you didn't have to choose one problem to work on and stick to it even when you were getting nowhere.
For me, the long afternoon break gave me time to think about the problems on my own (while relaxing in a deck chair with a beach view and catching up on the internet) so I could come back to the discussions with fresh ideas. I heard several people remark that having two intensive sessions so far apart made it feel like we were getting in two days of work for every day of the workshop. The hope of being invited back to such a pleasant place also provided some motivation to work hard. And group social activities such as our meals together and the daily meet-up on the beach at sunset to watch for the green flash (sadly, not in evidence this year) helped build cameraderie and made it easier to join in on research discussions with groups of people you might not already know.
I'm not yet sure in what form and when the results of this all will appear (so I'm being intentionally vague about exactly what we discussed) but expect to see some new names in the co-authors of some of my future papers.