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With half of her Lafayette experience still ahead of her, Blerta Shtylla ’05 (Tirana, Albania) impressed more than a few researchers during the Summer Undergraduate Research Conference in Mathematics at Ohio State University last month.
Addressing an audience of faculty and students from around the United States, Shtylla presented results of her work on knot theory this summer with Louis Zulli, assistant professor of mathematics, in the National Science Foundation’s Research Experience for Undergraduates. Hosted by Lafayette, the program involved four students from Lafayette and others from Princeton, Johns Hopkins, Boston University, Shaw, St. Joseph’s, California State-Long Beach, and North Carolina State.
“Blerta’s talk was outstanding,” says Zulli, who regularly shares his own research through journal articles and conference presentations. “She discussed complex mathematics clearly, with poise and enthusiasm. There were many questions — from both students and faculty — and she handled them quite well. After her talk, while I was busy with other things, Blerta discussed our work in more detail with several of the experts in the audience. Her talk was openly praised by both students and faculty, and several of my fellow topologists privately confided how impressive she was, and expressed surprise when I told them that she was not yet a junior.”
Shtylla says Research Experience for Undergraduates was a great learning experience that exposed her to new areas of mathematics. Her participation in the program was funded by Lafayette’s EXCEL Scholars program, in which students assist faculty with research while earning a stipend.
“As a math major, I found that extremely enriching,” she says. “Preparing for the research was a great learning experience also, because I had a chance to explore the topic at my own pace and read papers in the field. Then during the summer I got to study some interesting cases of knots and learn how research is done in mathematics. The greatest thing this summer was having the freedom to pursue my own inquiries with the guidance of my professor and raise questions.”
Exchanging ideas while working with Zulli on a one-on-one basis and becoming more confident about her mathematics knowledge was intellectually stimulating, notes Shtylla.
“I learned more about how to think as a mathematician, went over lengthy math papers, practiced some proof writing, applied some of the knowledge learned in other math classes, and most of all, I learned how to be ‘friends’ with Mathematica and gain confidence in how to use that software. Overall, I learned a great deal this summer, not only about mathematics, but also how to think as a researcher — knowledge that will be inevitably useful in the future, and best of all, I got paid to do this too!”
The knot theory research she conducted is part of the larger field of topology, which deals with the “intrinsic shape” of objects, ignoring such issues as size and curvature.
“For example, to a topologist, a cookie and a muffin have the same ‘shape,’ but a donut is different because of the hole in the center,” Zulli explains. “In knot theory, we study the different ways in which a simple closed curve (a ‘knot’) can be positioned in three-dimensional space. The fundamental problem of knot theory is to classify knots. That is, one would like to have a complete ‘list’ of knots, and also a process for determining where on the list a given knot falls.”
Zulli illustrates with the analogy of collecting wild mushrooms. Those who study them want to have a complete list of species and, when they find a mushroom, to be able to identify it. What species is it? What’s interesting about this species?
“Despite more than 100 years of research, an effective classification of knots still eludes us. In addition to its importance within topology, knot theory is being applied in biology and chemistry (long molecules like DNA can actually be physically knotted), and there are many connections between knot theory and theoretical physics.”
When it comes to describing Shtylla, it’s hard not to “gush,” admits Zulli.
“She’s certainly one of the finest students I’ve met in a long, long time,” he says. “She’s very bright, very hard working, reliable and articulate. She loves learning, and she’s interested in so many things: mathematics, science, medicine, languages (she speaks four). I’m convinced she’ll be outstanding in whatever she chooses to pursue. She’s been a pleasure to work with, and I’ve really enjoyed getting to know her and learning more about her fascinating country and culture.”
Shtylla’s excellence has been recognized with Lafayette’s Eugene P. Chase Phi Beta Kappa Prize, awarded to sophomores who have demonstrated scholarship as first-year students. She says that serving as a teaching assistant for calculus labs and tutoring students in Calculus Calvary last year were great opportunities to use the knowledge gained at Lafayette to help her peers.
“The fact that I am at Lafayette and have had the chance to explore and learn and challenge myself continuously is a highlight in itself,” she says. “I have always had a lot to do, but the best thing is that I have really enjoyed what I am doing, so it’s never felt like too much.”
A pre-med student, Shtylla served an externship two years ago through Career Services with a pediatrician in New Jersey. “That gave me a great opportunity to witness a doctor in action and to make a decision about my future career plans,” she says.
Shtylla is a returning resident adviser in Marquis Hall and treasurer for International Students Association. She is “very excited” about declaring a minor in bioengineering soon.
Zulli is a reviewer for the journal Mathematical Reviews and a referee for Mathematics Magazine. A member of Phi Beta Kappa, he earned the Outstanding Faculty Associate Award while teaching as the G. C. Evans Instructor of Mathematics at Rice University.