Kurt Vinhage, who got his Bachelor's in Mathematics at FSU and is now a graduate student at University of Pennsylvania, may joke about missing the Quizno's near the Love Building, but what he really misses about his time at FSU is the people. As a PhD student in his third year at Penn State, Kurt is using what he learned in FSU's math department to teach students and pursue his research interests. His advisor, Anatole Katok, with whom Kurt works, focuses on rigidity of higher-ranked dynamical systems and rigidity of Weyl chamber flows. As he explained, "In a classical dynamical system, time can be a discrete or real parameter, but in both cases it's one-dimensional. In a higher-ranked system, it's multi-dimensional. The work I do is classifying, showing rigidity phenomena that occur -- measurable rigidity, differentiable rigidity, structural stability." And he's doing what he loves, drawing on his undergraduate studies: "I really like the subject because it has a unifying element to it. To prove what I want to prove you have to use tools from algebra, geometry, and measure theory, and there are very few subjects where you use such a variety of tools."
For Kurt, a precocious curiosity towards mathematics predates his time at FSU. It goes all the way back to his childhood. He said, "I always liked math and was always fascinated by geometry -- so much so that in middle school, I started keeping a notebook with formulas for approximations for pi. In high school I asked my father for his calculus textbook and started reading that." FSU provided an environment for Kurt to foster those ambitions. Dr. Hurdal, his Calculus 3 professor, encouraged him to consider graduate school, and he had the opportunity to take part in a pre-graduate program called MASS (Mathematics Advanced Study Semester) at Penn State.
After working through most of the math courses offered at the undergraduate level, Kurt was able to work closely with faculty to keep digging. He explained: "The FSU department did a really good job of making sure I always had a new course to take and new material to work on. There was a lot of personal attention. I did an honors in the major under Dr. Mesterton-Gibbins, and I also had the opportunity to do a minor research project with Dr. Hironaka." Kurt made it clear that the faculty's investment in his success and support of his curiosity did much to prepare him for his current undertaking. He discussed his research projects at FSU, saying, "I got a feel for how to think about problems that have never been solved before. When you take a course, you look at problems with solutions. But when you start a new project, you don't know what tools you'll need. It's a new way of thinking, and being exposed to that at FSU was a great help."
Kurt has had the chance to add teaching to his skills, as both a teaching assistant and a lead instructor. While teaching Introduction to Linear Algebra, he was glad to see "the material was accessible to students who hadn't yet taken Calculus 1." He's clearly enjoyed his teaching time, and looks forward to more. Whereas research can be solitary or abstract, teaching provides an opportunity to make connections between the field and the rest of the university. Kurt explained, "Communication between disciplines is important in establishing the growth of knowledge, and being able to teach at any level is a good quality in any mathematician."
Kurt had advice for those students considering graduate work in mathematics. He emphasized the benefits of a personal investment in one's studies, saying "You can get a degree by going to the courses. But there's so much more to be gained from the FSU experience. If you don't take advantage you're really cheating yourself." How? He recommended sitting in on graduate courses, to get an idea of what's coming, and getting to know faculty -- "Don't be shy about it."
When asked about his thoughts concerning the future of the FSU math department, Kurt was glad to know that a greater variety of courses are being offered at the undergraduate level. He was also excited about new faculty and new research projects going on. But the future of the field in a broader way? He'd like to see more people finding a balance among research, the historical appreciation for scholarship, and the new work being done. He loves what he's doing, considers himself lucky, and hopes others will follow in his footsteps. He said it best: "To get to think about the problems you want to and work on the problems you want to is a great luxury."