This is a response to Adriana Salerno's post about workshops on PhD + epsilon. She asks at the end, "Do you like workshops as much as I do? Have you had any great results come from a workshop? Are there any others that you can recommend to people?"
Short answers: I love workshops and summer schools!
Workshops give a great chance to really work on mathematics (or coding, if it's a Sage Days-type workshop). The AIM-style workshop Adriana mentions is one of the best. I have attended one AIM workshop and they allow so much time to really get into the math -- I am still working on problems and working off notes that were written down there. (Yes, AIM, when I finally publish the paper inspired by that problem I'll let you know and you can get some credit for it!) They are great opportunities to talk with mathematicians at a very deep level and figure out what needs to be done in your field and whether you could do it.
I think these are best, though, for people who know something about their topic and are ready to dive in. What if you want to learn about a new topic instead?
If you're a graduate student, check out MSRI Graduate Summer Schools in particular and MSRI workshops in general. The summer schools are usually two weeks long and are immersive experiences: you are completely bathed in the mathematical topic at hand. It's a good thing. The best summer schools have homework exercises that you can try to slog through over a beer or something non-alcoholic, depending on your taste; you should always try to do the math you're hearing about. I've had good experiences with all MSRI events I've attended.
The IMA also puts on various workshops, and has trended toward putting on a pure-math computer-oriented workshop each summer recently (Macaulay2 and Sage, for instance, each had a week-long workshop in recent years. IMA workshops tend to bring together people from different areas to a greater extent than AIM or MSRI workshops, it seems to me. Another place that seems to be interested in a certain level of interdisciplinarity is ICERM which looks to have some cool workshops coming up.
I do like workshops with time built in for doing math or doing exercises or discussion better than the conferences that consist mainly of an intense number of talks separated only by thin coffee breaks, but those too have their purpose.
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