I have just returned (well, sort of returned) from an amazing week at the Banff International Research Station for a Focussed Research Group workshop on Effective Computations in Arithmetic Mirror Symmetry. A great research problem, collaborators who are both smart and fun to be around, and a backdrop of the Canadian Rockies (with an occasional elk sighting): what else could anyone want? In this blog post, I want to tell you a bit of how I came to be there in the first place, as one of the organizers in fact, and what being a part of an FRG is like.
I guess it all comes down to networking. Specifically, to a very random incident: I went to SACNAS in 2010, and tried to attend some of the math talks. One of these talks was actually very close to my Ph.D. thesis topic, and in fact some of the computations described were essentially the same. The difference is, my thesis was about number theoretic questions (counting rational points on varieties) and this talk, given by Ursula Whitcher, then a postdoc at Harvey Mudd, had an algebraic geometry and mirror symmetry point of view. I walked up to her at the end of the talk, and we started talking about our research. And this is essentially how the project on computational arithmetic mirror symmetry was born.
Of course, we started talking to other people, and quickly it became clear that it wasn’t enough for the two of us to work on this project. In other words, we needed help! And that is when we had the idea to hold a small workshop, which led us to the Focussed Research Group grants offered by BIRS. We enlisted Charles Doran, Ursula’s Ph.D. adviser, to help us write our application (he had many great ideas and questions we hadn’t even thought about). The three of us picked five more people to attend and we were set! A few months after submitting our application we were told it had been accepted.
Last week our motley crew finally met. The group consisted of some number theorists, some algebraic geometers, and some mathematical physicists. Since our backgrounds and levels of expertise were quite varied, we started with a few talks and informal discussions. It was clear right away that not only what we knew was varied, but also what we wanted to know. I think we found some common ground and made some good progress, but I know each one of us felt out of place at one time or another. On the other hand, it was clear that this problem is a good one, precisely because very few people understand all aspects of it. I mean, that is exactly when you need to assemble a group of people of diverse backgrounds to work together in the same place. I’m just really happy that we made some progress, and more importantly that it seems like only the beginning of a fruitful research plan. We are already planning future meetings and I’m looking forward to seeing this group again.
The setting at BIRS could not have been more ideal. The views were inspiring, the facilities were in top shape, and the food was delicious! It is really a perfect place to get away from the world and just sit down and do some math. The fact that the group was very lively and got along well was the icing on the snow-covered cake.
You may have noticed I’m avoiding talking about mathematical details. There are many reasons for that, but in particular, this is not a blog about math, it’s a blog about being a mathematician. If you do want details, just click on the link I gave above for a description of our project. Hopefully in not too long we can share some of our progress in paper form!
I want to end this post by reiterating that if you have a research project and a few people you want to work with, this setting is pretty perfect. If your group is smaller than five people, you can instead apply for the Research in Teams. I’m really happy we did this, and I hope more people take advantage of this wonderful opportunity to do math in a beautiful place.