Discovering the Small-World Network*

One of the hardest things about transitioning from a large research university to a small liberal arts school is the sense of mathematical isolation. At UT Austin, I was accustomed to TWO weekly Algebra/Number Theory/Combinatorics seminars, a large and active Number Theory group (including world-famous mathematicians like John Tate), and many other postdocs and students to talk to about my own research. When you come to a place like Bates, where there are six other faculty members in your department, of which only one is a number theorist, you can start to feel like there’s not a lot of people to talk to. This makes it easier to lose a little bit of the momentum you brought with you from grad school or your postdoc. The good news is that there are things you can do about this, and I will share some that have helped me stay connected to the mathematical world.

Go to conferences.

If you have a heavy teaching load (which is the case at most of these small schools) this one might be difficult. You should still try to go to a few of these at least at the beginning of your small liberal arts school career. My first year here, I attended the Maine-Quebec Number Theory conference (which was a great way to meet the local number theorists and get them to know me), the Joint Math Meetings (although that was mostly because of Project NExT, which will be a blog topic soon), the Arizona Winter School, a workshop on Counting Points at the CRM in Montreal, and an MAA PREP workshop at Williams College on teaching Algebraic Number Theory. Some of these were right up my alley research-wise, and others were more teaching oriented, but all provided me with a great sense of connection and allowed me to keep up an active network. I always feel energized and excited after a good conference, and you never know what some of the friendships you make will yield (Collaborators? Future advisers for your graduating seniors? Future hires? Best friends forever?).

Give talks.

Ideally, you would also talk at the aforementioned conferences, but that’s not a requirement. In fact, some of the people you meet might invite you to talk at their schools. Thanks to the connections I made at those conferences, I got to give talks at Wesleyan, Vassar, Brown, and MIT.  I also got to give talks at Bowdoin and Colby, mostly because there is a really good relationship between the three math departments, but I will talk about that more in the next item. Giving talks is good for you in many ways, but in my case, it helps me keep thinking about the research I’ve done (even if in the middle of the semester it’s really hard to keep doing much research), and it lets other people know that I exist and what kind of research I’m doing. I have a few potential collaboration projects that have started with me giving a talk at a conference or seminar (or going to see someone else’s talk, this is important too!).

Start your own seminar!

At Bates, we have an ongoing department seminar that meets several times in a semester. But what happens more often than not is that our own faculty gives the talks, and none of us really know that much about each other’s research areas. In my department, there are two number theorists, one algebraic topologist, and one combinatorist (is that the right term?). That’s not a lot of people to start a more focused seminar with. But if you look around you find Bowdoin and Colby close by, with about that many people who are interested in similar things, and if you put all of us together you might get a decent-sized research group!

Last year, a few people from Bates, Bowdoin and Colby got together and applied for -and won- a grant from the Mellon Foundation (who had already given $300,000 to the three colleges for “faculty enhancement”). The money we won (I forget the amount!) now goes to the CBB (I guess BBC was taken?) Algebra, Number Theory, and Topology Colloquium Series. Peter Wong, the Bates PI for this grant, told me that the idea was to “bring very good researchers” in the field, who can also give very good talks, and have them talk to the faculty and advanced undergraduates. This is meant to energize the faculty (like I said, good talks make mathematicians excited about doing more mathematics), maybe give us some ideas on future research, and ultimately bring experts to Maine and foster interaction between the three departments and between us and the rest of the mathematical world.

The grant started in January 2011 end expires June 2012. The first event we had was a one-day “collaboration conference”, which included an introductory talk and two advanced talks (one by yours truly) and geared towards showing a couple of facets of current number theory research by people in our group. We later had invited talks by geometric group theorist Kevin Wortman (University of Utah) and number theorist Ken Ono (Emory University). Ono’s visit was particularly exciting to me (as a number theorist) and has given me some ideas on problems to think about.

There are similar seminars out there, like the Five College Number Theory Seminar in western Massachusetts, and the Claremont Colleges Algebra/Number Theory/Combinatorics Seminar, in southern California. If you find yourself in a small place and would like to start some sort of seminar/research group, just look around you. I bet there will be other people in your situation not that far away.

Just stay connected!

Maybe you’re a loner mathematician that is happy living in the woods and doing your own research without talking to other people. In that case, you probably wasted your time reading this post. But if you’re like me, and most mathematicians I know, you need to talk to other people about math, you need to see people talk about math to get ideas, and in general you need to stay connected to the larger mathematical community. I just listed some of the things that have helped me, and I invite you to post any other ideas you have about how to stay connected.

*According to Wikipedia, “in mathematics, physics and sociology a small-world network is a type of mathematical graph in which most nodes are not neighbors of one another, but most nodes can be reached from every other by a small number of hops or steps.” I like this as an analogy of what I’m talking about. Even if you’re slightly isolated, there is always a small number of hops or steps that will get you in touch with the larger mathematical community.

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5 Responses to Discovering the Small-World Network*

  1. Keenan Kidwell says:

    First of all, I wanted to say I like reading your blog, Adriana (I usually don’t have the patience for blogs but I find yours keeps me interested). I was just wondering, you said you went to a workshop on teaching algebraic number theory. What was that like? Was it aimed at teaching graduate students? Undergraduates? Do you think you’ll get to teach an ANT course at some point?

  2. Peter says:

    You could even take your seminar to the next level via video.

    I’m sure most people have used a video chat (skype, google chat etc) to collaborate. But it’s not that complicated to actually broadcast your seminar live to go beyond the 1-on-1 communication of video chats. You don’t even need fancy video-conferencing equipment, just a decent camcorder hooked up to a laptop and free services like ustream and justin.tv.

    You can pretty much have a worldwide seminar whenever you want.

  3. Ali says:

    Thanks for the word of advice. What you describe is equally applicable to mathematicians working in developing countries.

    On a side note the right term is “Combinatorialist”.

  4. Greg Coxson says:

    Dear Adriana: I love your blog too. I work in industry, and have had the terrific opportunity to coordinate seminars at two different companies. There is something about seminars outside academia that is kind of special. There are often really interesting problems that arise that cannot be pursued due to tight project deadlines and budgets. Seminars allow such problems to “live”. I have come to think of it as being similar to a concept in bio-diversity — the richness of animal species is enhanced in an ecosystem if niches are preserved for species to hide out and make their homes. But there is an additional positive aspect of such seminars and that is the effect on the morale of attendees. My experience is that it enhances enjoyment of the work experience because week by week or month by month, you see just how rich and interesting your chosen profession is. All the best.

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