Talks vs. poster presentations: Which is better for advertising your research and building research networks? I'm looking into applying to present at a conference for undergraduates in mathematics this summer. When I apply, I have to either apply to give a talk (~20 minutes) or present a poster.

From what I've read on this site, it seems posters are often looked down on relative to talks, especially in mathematics. However, one advantage of a poster session is that I can have a back-and-forth discussion which is impossible in a talk. I think this is especially important for my research, since the computations in the subject are notoriously tricky and will trip up even experts if they aren't paying close attention to the details.

What are the relative advantages/disadvantages of each format? Which is a better way to advertise my research and network with other researchers in my field?
It depends on what you want to do. If you feel like at this point in your research it would be more beneficial to converse than to present, then I'd say that a poster session is the right venue for you. It's true that talks are considered a bit more prestigious than poster sessions, but you really should go with what you think will be more valuable for you, and for the conference attendees.

It's worth noting that you could always do a poster presentation this year, get the feedback that you covet, and then return next year to do a talk, and let everyone know how your research went over the subsequent year. That kind of progression is not a bad thing.

Also, if you are in the early stages of your research, it might not be ready for a talk. When I attend a conference talk, I'm expecting there to be some significant findings. Sure, talks might be more "prestigious," but, if there are some holes in your research, you could end up discrediting yourself. People aren't expecting the same level of maturity in the research during a poster session. So, as I said before, forget the prestige aspect, and choose what is more fitting based on your goals, and on what you have to share at this point in your research.