# University of Vermont

### Featured Faculty

#### Greg Warrington

Princeton and Harvard educated, assistant professor Greg Warrington is a member of the CEMS Mathematics and Statistics Department, and he may be the only member of the UVM community who considers juggling a form of meditation. Greg sat down recently for an interview:

SPIRE: Professor Warrington, tell Spire readers a little bit about where you are from.

WARRINGTON: I grew up in southern New York in a town with excellent public schools. It was a very comfortable upbringing. I played all of the usual sports and liked school. My parents (my dad worked in marketing and my mom was a homemaker/librarian), did everything they could to ensure that my brother and I had the best upbringing possible.

I've always loved to read, and I loved puzzles of all kinds. Word puzzles, jigsaws, logic puzzles. I still come up with word puzzles in my idle time, but most of them are too complicated or esoteric to be worth sharing. (An example of an esoteric one: "Why is 'selflessness' Fibonacci's favorite word?") I really enjoy figuring things out and admire elegant solutions to problems.

SPIRE: We've heard from several sources that you are a fantastic juggler. How did that come about?

WARRINGTON: I became interested in juggling when I was in middle school. My older brother knew people in the juggling club at my high school and encouraged me to learn to pass clubs so that he would have someone to pass with. It's the perfect hobby for me.

Juggling is my form of meditation. The feeling while smoothly running a pattern is magical. Everything is happening too fast to think about any individual ball. And you certainly can't afford to look down at your hands. But in front of you is a pattern that is beautiful in its regularity and symmetry.

Juggling can also be really good exercise. It's a nice break from sitting and thinking. It wasn't until college that I learned about the existence of a mathematical language for juggling. It's akin to musical notation but differs in that it makes a distinction between valid and invalid patterns. The language is a great example of the interplay between art and science, a relationship to which I've always been attracted. I actually have one mathematical research article that investigates the behavior of a person juggling randomly.

SPIRE: When you were in high school, what — besides juggling — were you planning to do with your life?

WARRINGTON: I didn't give it much thought. I knew I would do something related to science. There was a big IBM presence in the area, so I certainly had examples of that career path amongst my friends' parents. We didn't live close to any universities, so none of friends' parents were professors. I was definitely more interested in chemistry and physics than mathematics, though. My college math courses brought out the beauty and power of mathematics in a way that calculus never did for me. Now I love calculus, but that has only come with a better perspective on why it is such a monumental intellectual achievement and on the paradigm shifts it led to.

SPIRE: So, you were into chemistry and physics in high school, but it was mathematics that you decided to pursue in college?

WARRINGTON: Yes — I have a BA in mathematics from Princeton. I was certainly very attracted to some of the smaller liberal arts schools but wasn't sure precisely what I wanted to do scientifically. I decided the larger size of Princeton would be better equipped to absorb any changes in my plans. And it was. I didn't even take a math course my first semester, but that's what I ended up majoring in. And I got an excellent preparation in mathematics while also being able to take advantage of Princeton's depth in the liberal arts.

My decision to go to Harvard for my PhD was based on it being a great program and in a place I wanted to live. The department gave us a lot of flexibility to pursue our interests and degrees in a manner best suited to our own needs. I am very grateful for the opportunities I had there.

SPIRE: Dean Grasso and the faculty have chosen Complex Systems Analysis as the research thrust for the College. What is your take on Complex Systems?

WARRINGTON: I think it's an excellent choice and a very exciting area. The pace of progress in some of the pure mathematics I am interested in can seem glacial to scientists working in other fields. It is not uncommon for me to look up references from the seventies or even earlier. I'm excited to bring my perspective to a younger field of such growing importance in our everyday world.

WARRINGTON: Much of mathematics can be thought of as being primarily about the relationships between objects rather than the objects themselves. This is one of the aspects of mathematics that enables it to connect so many seemingly disparate areas. Often you can work with these relationships without even knowing what the relevant objects really are. But having concrete objects to work with can be very useful too.

So a lot of my current research looks for the concrete objects underlying fundamental abstract relationships. The point is that with these concrete objects in hand, we can in turn get a better understanding of the original relationships. I do a lot of computer investigations to help guide me and look forward to taking advantage of the VACC.

My particular focus is on questions relating to permutations (i.e., reorderings). Permutations arise in such varied contexts as mutations in DNA sequences and cryptographic algorithms.

SPIRE: How would you characterize your teaching philosophy?

WARRINGTON: I see teaching and research as parallel endeavors. I'm constantly seeing new connections and learning new facts when I think about how to present material to students. The things I'm learning have already been figured out by others, but they're still new to me. And if I'm excited about what I'm learning, that energy will automatically be conveyed to my students. In research, the primary difference is that I'm working on uncharted ground.

There is a natural tendency to boil the topics in a course down to the essentials. This is efficient, but over time it can suck the life out of a topic. I think the best thing to do is to push against this and ensure that the connections to other fields and ideas are kept healthy.

I think all knowledge can be made exciting. My challenge is to convince my students that what I'm teaching them is beautiful, useful and interesting.