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Maggie Ryan, a rising junior, is spending the summer working on an Emerson project that investigates non-commutative algebra, which is a type of algebra that can help solve one-way information problems and has applications in quantum physics. Associate Professor of Mathematics Courtney Gibbons is faculty adviser on the project and Visiting Assistant Professor of Mathematics Branden Stone is assisting. Ryan is one of 200 Hamilton students who are conducting summer research or completing an internship supported by the College.

##### What are you researching?

We’re still piecing it together sort of, because the initial idea was to be working with non-commutative algebra. So, a commutative space is … you know how three times two is the same as two times three? Imagine if it wasn’t. That’s the kind of stuff that I’m supposed to be working with.

…We’re going to be looking at these things called the edge ideals. So if you have, (for example) a graph…just imagine two points, like an x and y, and a line connecting them. That’s a graph. And usually when people work with graphs, they’re working with ones where going in one direction is the same as going in the other direction, so x to y is the same as y to x, and that’s the equivalent of commutative stuff. What we want to be working with is graphs where it’s directed, so going one direction does not equal the other direction.

##### What are your day to day responsibilities?

Really, we meet up at some point in the morning and go over whatever (faculty advisers) told us to do the previous day. If we have questions, we ask them. They either explain or they ask us questions until we figure it out ourselves. And then they’ll introduce some new concepts and give us an assignment to be done the next day. For the past while, it’s been more or less like a class, but I have a feeling that the way it’s going to proceed is we’re going to be doing more independent stuff.

##### How did this become an Emerson project for you?

I guess I was really excited by the idea of getting to contribute something new to mathematics.

Majors: Math and Geosciences
From: Montauk, NY
High School: East Hampton High School

So the idea that [Gibbons] had posited about the non-commutative stuff, there’s not a lot of work that’s been done about that already, so the idea of getting to do something new that’s breaking new ground was very exciting.

##### Why did you choose Hamilton?

Of the colleges that I visited, this was the one I was most easily able to imagine being home. I got a very nice vibe from the place. The people seemed like people I wanted to be around.

I think I was walking under the arch part of the student village, and I saw someone riding a bike who had long, flowing blue hair and I was like, “Yes, this is what I want.”

##### Is there anything else you want people to know?

I guess something nice to put out there would be that I know that I know that I am an intelligent person. I wouldn’t be here if I wasn’t, and I wouldn’t be doing this research if I wasn’t, but I’m not someone who waltzes into class, doesn’t take any notes, and still does super well on all the assignments. I work and struggle and I’d say I’m slightly above average. You don’t have to be any superstar to be making contributions. You can just be average and still do something really cool, which is what I’m feeling here.

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