I am a beginning graduate student in mathematics. My university holds regular seminars in different areas of mathematics, and I try to attend all of them. I like getting exposed to different areas of research I did not know of, and get updated about recent developments. Listening to different speakers on different areas of mathematical research has greatly helped me become more confident in approaching new areas with new thoughts.
Often the researchers pose open problems. I note those down and after returning home, I try to read up about them but usually I find there are lots and lots of background material to cover and certainly I would have to spend a lot of time reading things up to get to the point where the speaker leaves something as an open problem. Please note I am a beginning graduate student.
Even if open problems have not been directly posed, following the speaker's work may eventually lead me to solve related problems in the area. Unfortunately the time taken scares me and essentially those notes get lost.
I am not even sure if the system I am following is proper. How does one get the most out of seminars? Or, what message is a seminar really intended to convey? Just a demonstration of some work done by the speaker, to be validated (at least at face value) by the audience? Or expose the audience to areas they can work on? In the latter case, how does one keep track of all the information obtained from seminars? A disciplined approach would be solicited.