Photos by E. M. Sweeney Jr.

Liz Bouzarth ’03 untangles the threads that link mathematics and physics Knot Fun By Jillian Cohan

There’s no Target store in Lancaster, Pa. Many upscale outlet stores, but not one hip discount retailer. So Liz Bouzarth ’03 makes a point of stopping at the Target in York on her way home for semester breaks.

In jeans and a pistachio-colored sweater, Bouzarth exudes youthful energy. The tall brunette has a fresh-faced appeal that’s somehow familiar. She could be your daughter, your niece, the girl next door.

“I love pink,” she says, her fingers brushing a heart-shaped picture frame. Looking over the Valentine’s Day merchandise, she confesses that her boyfriend, a physics major, often teases her about her romantic side. Standing among the hearts and flowers, she describes him as a serious, scientific type. As she contemplates a rose-scented candle, she explains that with her it’s different. People often are surprised when she tells them she’s a math and physics major. She thinks it must be because “there’s nothing stereotypically scientific about me from the outside.”

She’s right. She looks more like the women’s tennis-team captain than a Phi Beta Kappa inductee.

She’s both, just as apt to spend hours on Dickinson’s hard courts as in the Jacob Tome Scientific Building working on her honors thesis.

But you can’t see her genius. It lives inside, in her gray matter.

Moving on to the housewares section, she picks up a vibrant placemat that would be at home in a Tiki bar. “This is cute, sort of retro,” she says, mentally furnishing her grad-school apartment. Next to the placemat, she notices a set of Tiki-inspired napkin rings.

Inside, in her gray matter, she makes a connection between the shape of the napkin rings and knot theory, the theoretical mathematics field that forms the basis of her senior research.

Knot theorists would describe a napkin ring as an “unknot,” she explains. The simplest of all knots, it’s basically a circle or a closed loop. Hair ties, like the elastic she wears around her ponytail, are another easy-to-visualize example.

You’ll probably find more examples of unknots here, among the Valentine’s gifts and kitschy home décor, than you will in Dickinson’s math classes. But knot theory offers fertile ground for undergraduate research. Just ask Bouzarth and her two senior-theses advisers, physicist Hans Pfister and mathematician Dave Richeson.

Bouzarth adds to her slate of activities a job as teaching assistant in two Workshop Physics classes.

On the second floor of the science building, Pfister gestures to the left-hand wall of his office. “Would you like to see my toys?” he asks. The incarnations of plastic run riot across the shelves, their purposes mysterious to the uninitiated. An associate professor of physics and chair of the physics and astronomy department, Pfister would be just as comfortable doing magic tricks at birthday parties as he is in the lab, teaching Workshop Physics. His delivery is perfect: Introduce trick (or lecture concept), demonstrate it with one of his many toys, bring volunteers from the audience to try it for themselves, then encourage them to try again when they don’t get it right. He never reveals the answer, pushing his students to make their own discoveries.

To illustrate the concepts he and Bouzarth used in their research, Pfister pulls out a length of rope, three electrical cords (black, white and red), and two pencils lashed together with rubber bands to form the shape of a cross. These are the “high-tech” tools they’ve used to explore a link between knot theory and his area of expertise, plasma physics.

Plasma, he explains, is an ionized gas also known as the fourth state of matter. In the real world, plasma physicists and knot theorists seldom communicate, but his research with Bouzarth brings together concepts from both fields. Their project uses Reidemeister moves (a basic knot-theory tool to determine if two knots are equivalent to each other) to measure the knottedness or twistedness of bundles of magnetic fields that occur in the plasma of outer space. The measure of this knottedness is called magnetic helicity. Their research, which they have submitted to the American Journal of Physics, proves that helicity doesn’t vary in spite of the magnetic fields’ movement. The project is more complicated than that, as Pfister demonstrates with the electrical cords, but you’d have to spend hours playing with the toys in his office to get a clear picture.

Just a few yards away, in the north wing of the science building, Dave Richeson’s office offers an oasis of calm. Where Pfister’s toys crackle with kinetic energy, Richeson entertains himself in a more cerebral manner.

“I was the nerdy kid who always did puzzle books,” the assistant professor of mathematics recalls. “Math has always been fun for me.” Yet he knows that’s not the case for everyone, adding, “Many lower-level teachers don’t understand that math can be fun. A lot of the coursework is dry, but a lot of the concepts, like knot theory, are fun and, in their essence, are pretty easy to understand for people without advanced training.”

That said, pick someone off the street and ask him to define a Reidemeister move. You’ll get a blank look in return. But show him the three moves, which help knot theorists remove false tangles from knots, and it makes sense.

When they were teaching themselves knot theory, Richeson and Bouzarth used her hair elastics to puzzle through the Reidemeister moves. As their understanding grew, they also played with ribbons and telephone cords, which helped them develop five new moves that are applicable to the twisted magnetic-field lines Bouzarth examined in her physics project.

The strands of mathematics and physics are similarly twisted together throughout her research, an aspect of the project that Richeson relished.

“Something at Dickinson that people value is being able to see connections between different fields. A thesis like Liz’s, where there are math and physics angles, shows a drive for those connections,” he says. “Until now I thought that crossing borders didn’t pertain to me [as a pure mathematician]. Our work has been eye-opening—now I understand that it can apply to me.”

Their work together also has proved to him that Bouzarth is accurate when she says there’s nothing stereotypically scientific about her personality. Even though she’s a candidate for admission to 11 graduate schools and, as of late February, was accepted by all that had responded, the phrase “math geek” doesn’t spring to mind when he describes her. Instead, it reminds him of one of his favorite jokes:

Women’s tennis coach Becky Cecere calls Bouzarth “a quiet leader.” This season, her third as team captain, Bouzarth was one of only 70 Division III women to win the Intercollegiate Tennis Association’s Scholar Athlete award. She was the only woman in the Centennial Conference to make the list.

“How can you tell if a mathematician is an extrovert?”

“He looks at your shoes when he talks to you.”

Although he knows some shy mathematicians, Richeson says most of his students don’t fall into the extreme-introvert category. (For evidence, he points out that a good number of football players major in mathematics.) “My guess is that people who pursue a liberal-arts education are generally well rounded, so our math students are well rounded to begin with.”

Especially Bouzarth. She’s more than a math whiz. Teaching assistant, tennis captain, student senator—the list goes on.

“If there’s one word that’s overused at Dickinson, it’s ‘engaged,’ ” Richeson says, “but that’s what she is.”

Bouzarth is engaged in the community, too. For the last four years she has managed the Carlisle Tutoring Program, a volunteer organization that matches Dickinson students with area elementary and high-school students. As coordinator, she works with local guidance counselors, tutors and the parents of children in the program to make sure it runs smoothly. She also finds time once a week to make a tutoring house call to a high-school freshman in nearby Mechanicsburg, Pa.

On her way to the Target checkout counter, Bouzarth stops at a display of DVDs. After a grueling semester, she’s ready to indulge her romantic side with a movie. No tennis, no tutoring, no Reidemeister moves. Not today.

Without hesitating, she passes over the Oscar-winning biopic A Beautiful Mind in favor of Serendipity. Right now, the story of math genius John Forbes Nash Jr. holds less appeal than the twists of fate that unite two young lovers in the romantic comedy.

Standing at the checkout counter, she’s just another college student at home for break. On the outside she seems as simple as an unknot. You can’t see her genius.

But inside, in her gray matter, Bouzarth can’t help but imagine Serendipity’s plot line as a twisted, tangled knot for her to unravel. •