How does academics form discussion & study environments efficiency and effectively? As a student, I often read &amp; hear academics meeting in workshops to discuss problems in their fields with their colleagues, or with academics in other field etc.. As a Physics &amp; Mathematics student, I know how beneficial and enjoyable is discussing ideas with a fellow student, so I'm aware of the importance of such meetings.

However, whenever I (with other student) tried to form such a discussion groups, meetings, it always failed. Most of the time, we didn't have any specific problem at hand, and there was nothing to discuss. I mean after all we were learning the subject, and try to understand it; not to solve some particular problem. Of course, one can try to solve some "exercises" as a group, but most of the time those are just to verify we understood what we've learned, and their solutions are in web, so to a Physics/Mathematics students, there is almost no motivation, nor any joy, in solving or talking about them.

Similarly, I've seen various "study groups" in my department (within PhD student, PhD student with his/her advisor etc.) studying some topics together. Up to now, I always did self-studies alone, so knowing that doing this with a second or a third person would be much more beneficial, I also tried to implement such a study group, it also did not work, somehow.

Question:

How do academic meetings for discussions &amp; studying managed themselves in a way that it is useful for everyone, much more efficient compare to doing the same thing alone, and enjoyable ?
Let me suggest that there isn't any magic answer. Certainly not for efficiency. But a few things can help. 

Many (most?) such groups have some leadership. Often it is a senior professor and the group consists of other professors and some students.  Often the subject of the group is the main research interest of the senior professor and others are looking for their insights to help in their own research, likely in the same or a related area. Here the leadership is fixed and the cohesion of the group is guaranteed by the stature of that professor. 

Student groups are a bit different. If you can include a professor as leader, then you have a seminar, and many/most of the ideas come from the prof. That can be both stable and productive. 

Some student groups are driven by fear. In some universities, students that don't band together to study will likely be unable to understand everything needed in the course. Some law schools are like this. See the movie Paper Chase for a dramatic example. These are pretty stable and are a way for a group to share out a huge amount of readings and provide summaries for everyone. 

But if you want something more informal, what you need is someone to get it started with some ideas to study and also some commitment from a group of people. Of course the commitment needs to be sustained and that depends on the "work" of the group being mutually interesting. One way to manage the leadership issue is to pass it around. One way to do that is to have people contribute ideas for what should be discussed at the next meeting(s) and then vote among members on what should be pursued next. Whoever contributes the idea becomes "leader" for the discussion of the idea. That person probably has some commitment and the voting may add a bit more. But it is especially helpful if the proposer of the idea can give an initial outline and list of tasks before the meeting(s) at which the idea will actually be discussed. 

This, of course, isn't the only way to do things, but leadership and commitment are, I think, the two essentials.