Do you think a computational math student should go to student seminars about pure math?

Question

I am a first year graduate student with thesis topic on computational math, in particular inverse problem. Based on what I know, this area requires a solid background of functional analysis and numerical PDE.

Currently I am wondering what kinds of seminars I should attend. My department have weekly student seminars on analysis and theoretical PDE. Basically students presenting their work/research output to their supervisor. As this post and the great mathematician Terence Tao suggested, attending talks and conferences in different areas is beneficial. Hence I will try to attend other numercial analysis groups' seminars. But I was wondering whether it's helpful for me to attend those pure math seminars about analysis or PDE.

Though I found those seminars are interesting, my main concern is that being lack of suitable background, I may only be able to understand a small part of the seminar (a PHD student working on theoretical PDE once told me he can't understand his group-mates' seminar until his third year). The other concern is I will have less time for my own research . So in your opinion, what kinds of seminars I should attend? Shall I attend seminars in other departments (say physics or engineering) regularly?

Answer 1

You're not going to be able to determine which seminars are useful to you without going to some of them. And yes, some of them will be wastes of time. But I've gone to seminar series that should be extremely topical to me that never benefitted me directly, and some from peripheral departments that turned out to be very useful - as mentioned in one of the comments, even if you don't take away anything from the lecture, it's useful to know people. One day, you might find yourself in need of a graph theorist or some such, and it's helpful to have met them once, or be able to say "I saw your talk..." in an introductory email.

Also, selfishly, from an applied field, having applied participants in more theory heavy fields is helpful for teaching theory students how to present their topics to people outside their narrow subfield.

Answer 2

As an early-stage graduate student, you should go to whatever seminars seem interesting to you, so long as it isn't interfering with your research too much. A good way to think about this might be to budget a certain number of hours per week for seminars (I'd suggest 2 to 6 hours/week, depending on your load), and within that budget see which are the most attractive.

Over time, you will figure out which ones are most interesting and useful to you and which are not. It will no doubt shift with time, as well.

Furthermore, never be scared of going to hear a talk just because you aren't working in the area. You never know which interactions will turn out to be important. For example, half of my own research program ultimately stems from sitting in a lunchtime seminar series that had nothing to do with my thesis and that I attended just because it was neat to hear what was going on in that area. Ten years later, here I am.

Answer 3

Writing on inverse problems in particular, there is plenty of research of inverse problems for PDE from a pure mathematics perspective. For example, see the uniqueness results for Calderón's problem, enclosure method of Ikehata, and many results on hybrid data imaging (the recent book of Alberti and Capdeboscq is good).

There are a number of people who approach inverse problems for PDE from both theoretical perspective and the direction of numerics and functional analysis. There is plenty of space for collaboration and many conferences in inverse problems (e.g. Applied inverse problems, SIAM imaging, Inverse problems: simulation and modelling, Inverse days) have both theoretical and applied talks, and everything on the spectrum between them.

I would say that if the analysis talks discuss the equations related to what you are working on, or equations with obvious use in modelling concrete physical situations, then you should certainly consider listening to them.

For seminars in physics or engineering, you should check if the subject matter is related to your own research interests. If you work on medical imaging and someone is giving a talk on EEG, go and listen at least once so you know what kind of questions they ask in their research and how they present the information.