In the heart (or maybe spleen?) of Silicon Valley, in the parking lot of a very large Frye’s Electronics store, hiding in plain sight, you can find the offices of the American Institute of Mathematics (AIM). I had the privilege to be a part of a workshop there for a week in July, and also the fun of pretending I was working in some top-secret facility out of a spy movie. In this post, I will talk about my experience as part of REUF 3 (the third installment of the Research Experiences for Undergraduate Faculty), and about participating in workshops in general.
As the title may suggest, the REUF workshop is intended for faculty in primarily undergraduate institutions, and the purpose is twofold: to give faculty new research problems that they can pursue themselves but also problems that can be suitable for research with undergraduates. As a new(ish) member of a small liberal arts college, these are two issues I have struggled with, especially the second, since my research (which so far is mostly extending some thesis work) is too complicated for undergraduates. The workshop included some discussions on how to mentor students doing research, how to find funding for said research (like for REU’s), and the different places at which one could present said research and take one’s students. But most of the time was spent working on open problems.
The morning of the first day there were four introductory lectures, which served to give background information and also suggest some open problems. Topics were chosen from graph theory, linear algebra, and group theory. The workshop had about 30 participants, and later that day we were split into four groups, according to our preferences (I think every person got their first or second choice). I was put in the graph theory group, led by Ruth Haas. The rest of the week was spent trying to come up with conjectures and to prove theorems. I am a number theorist, so trying to prove something in graph theory proved especially challenging. But what makes it challenging is exactly what makes so attractive for doing undergraduate research: you can find very difficult problems, but you don’t need a ton of background to be able to tackle them, which is not something I can say about arithmetic geometry. There was a pretty steep learning curve (for everyone in my group) when it came to writing clear proofs of the conjectures we kept making. I, for one, spent the first couple of days just drawing pictures, and I was only able to write something down later in the week (my proofs were still mostly pictures followed by explanations of my formulas, but hey, in five days I had formulas!). I’m pretty excited about getting to talk about these ideas to my undergraduates in the future, and just by the feeling of being able to tackle a brand new problem that has nothing to do with my PhD research. On the last day each group got to present their results (see photo above for an action shot), and it seemed like all the other groups were just as excited and successful as ours. You can find more details and the final reports of each group by going here.
This is where I think that workshops are sometimes more useful than conferences. I still love attending conferences, I get to see lots of talks and meet people and maybe give a talk myself. But I’m starting to run out of things to talk about, since I seem to be doing much more traveling, talking and teaching than new research. A workshop gives you a chance to still learn new things and meet people but you get to start something new, rather than talk about something old. I have also found that I’m much more excited about math and research in general after a workshop.
In graduate school, I attended the Arizona Winter School almost every year (five times total). The most productive years were the ones where I was a part of a project (either officially or unofficially). The AWS had a pretty similar structure. There were four topics with a lecturer/leader, who gave four lectures during the week (but in this case they were much more linked my a larger theme, like Number Theory and Dynamics). The days were spent sitting in lectures (like having four classes every day) and then in the evenings the working groups got together and worked on problems related to the topics. On the last day, each group presented their results. As you can imagine, this was a pretty intense experience (and ate up your Spring Break), but I always felt it was completely worth it. I attended once after I started working at Bates (last year), but I think the best time for this conference is when you’re a graduate student.
Another workshop I attended was the Women in Numbers workshop at Banff International Research Station (BIRS). First of all, I recommend that everyone try to attend a workshop at Banff once in their lives. It is one of the most beautiful places to do math I’ve ever been to. Again, the structure was similar to that of the AWS, with more time for working in projects and less talks. It was also really exciting to spend a week with women number theorists talking about mathematics and doing mathematics, more than just talking about what it’s like to be a woman in math. This conference also gave me my only math publication to date (I’m working on some others, so I hope this will be rectified soon). There is going to be another installment of this conference this coming November, and I hope this will happen frequently from now on.
I haven’t been to as many workshops since I started working at Bates. Last summer I went to an MAA PREP workshop at Williams College for learning to teach algebraic number theory to undergraduates, which was slightly different. It was much more focused on teaching than research, but the structure was still quite similar, except that each group worked on planning a class. This workshop proved very useful for when I taught number theory later that Fall semester. A similar experience can be had by attending some of the workshops during the Joint Math Meetings, MathFest, the IBL workshop, or participating in Project NExT (which I will write about more later on).
I know there are many more workshops out there. The Park City Mathematics Institute has a great combination of research and teaching workshops every summer, for example. AIM and the other NSF funded math institutes host many variations of workshops, small working groups (like SQuaREs) and longer research programs. So now it’s your turn, dear readers, what workshops do you recommend? Do you have a great workshop story you would like to share?