How to get the most out of a seminar?

Question

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.

Answer 1

Mathematics is a highly specialized subject. Unless you're an exceptional mathematician, you are not going to do research in all of mathematics. You're not even going to do research in all of algebraic topology. Rather, you'll become a specialist in Glauznov operators on stable homotopy groups of Alberti spaces (example entirely made up).

As a (rather unfairly wrong but not without merit) starting point, you can assume that mathematicians are all solipsists interested only in their own problems. A seminar talk serves as an opportunity for one mathematician to advertise their problems and solutions in the hope that mathematicians in the audience will find the ideas they hear useful in their own work, or, even better, mathematicians in the audience will actually become interested in the speaker's problems.

The truth is that, as far as leading to publications is concerned, 95% of the seminar talks I go to will be a waste of an hour. However, it's also true that I won't solve 95% of the problems I make initial attempts on.

As a first year graduate student, you are not going to get much out of the technical details of seminar talks. What you can get (at least if the talks are good) is some flavor of different areas of mathematics so that you can make a more informed choice about what to specialize in. At some point, you will need to spend a year or two reading up on the background to something you hear about in one seminar talk. If you go to a lot of seminar talks, you will have a better idea of what you will want to end up spending a year or two reading up on. In addition, you will get some idea of the broader range of ideas that might be indirectly useful to whatever problem you end up working on, so that you will know which experts to contact and what to learn if you need help on some aspect of your problem that is not directly suggested in the prior literature.