# Dr. Cornelius Pillen on Research and Teaching

Dr. Cornelius Pillen, Professor of Mathematics and Statistics, grew up in the Black Forest of what was then West Germany. Studying abroad interested him as an undergraduate at the Albert-Ludwigs Universitaet in Freiburg, and for his junior year of college, Pillen matriculated at Trent University in Peterborough, Ontario, a small liberal arts college that had an exchange program with Freiburg.

After returning to Freiburg for two years and continuing his studies there, Pillen went abroad again—this time enrolling at the University of Massachusetts at Amherst. There, he earned his M.A. degree in Mathematics. According to Pillen, “I returned to Freiburg to write my thesis for the Diploma, the German equivalent of a Masters, but UMass had already offered me a slot in their Ph.D. program. So, I returned to Amherst and got my Ph.D. in mathematics. Then South offered me a job. That’s how I got here.”

Pillen started at South on a one-year appointment in August of 1991 and was hired for a tenure-track position the following year. His research focuses on representation theory and, particularly, the representations of groups. According to Pillen, “Groups are mathematical objects that capture and describe symmetry. For example, a square has eight symmetries. There are four rotations, each fixing the center of the square and rotating the plane by 0, 90, 180, and 270 degrees, respectively. There are also four line symmetries, or reflection symmetries. If we perform one of these symmetries, say a rotation, and follow with another, maybe a reflection, we obtain another symmetry from our list of eight. The eight symmetries together with composition form a Group.”

Pillen is now working with three other mathematicians on a problem that is closely related to his first thesis topic. “In calculus we teach our students how to find the line that best approximates a function at a given point, the so-called tangent line. In group theory we try a similar trick, approximate the group by a linear object called, a Lie algebra, named after the Norwegian mathematician Sophus Lie. The question my advisor first gave me as a thesis topic asked whether certain objects on which the Lie Algebra acts also allow for an action by the original group. I never made any significant progress on it but neither did anyone else. The problem has been around for over 40 years. It is extremely frustrating. Luckily, I had more success with other topics over the years.”

As a youngster, Pillen knew mathematics would be a major part of his life. In self-deprecating fashion, he says, “I think I loved math because I was lazy. In math you could figure things out by yourself, and you did not have to memorize endless amounts of seemingly useless facts and figures. I think early on I wanted to become a high school math teacher. But my studies abroad deepened my interest in the subject, and when the opportunity arose I decided to go for the Ph.D.”

For almost 20 years, Pillen has participated with Mobile-area high school and middle school students in the Department’s Math Circle. Pillen says his colleague, Dr. Vasiliy Prokhorov, Professor of Mathematics and Statistics, began the Math Circle at USA. According to Pillen, the Math Circle is “a blast” because “every Monday night we work math puzzles or play mathematical games with local high school and middle school kids.” The Department receives funding from the Alabama Space Grant Consortium for the Math Circle, and the students participate in the department-sponsored Mathematics Olympiad. He adds that the funding enables the Math Circle to “bring some well-known external speakers to campus to meet with the students and to take the Olympiad winners to the Colorado Math Olympiad in Colorado Springs.”

The Math Circle concept started in Eastern Europe, particularly in Hungary and the former Soviet Union. Prokhorov got the idea in the USSR. His wife, Natalya Prokhorov, teaches at the Alabama School of Math and Science and runs a Math Circle there. According to Pillen, the Math Circle at South was one of the first Circles in the United States. Pillen wants students “to see that math is not plugging numbers into formulas that nobody wants to remember. Math is solving problems, trying different approaches, thinking outside the box, working with others, making mistakes, being frustrated, seeking that Eureka moment.”

Pillen also participates in the Mobile Math Teacher Circle, which is part of a bigger program lead by Dr. Andre Green, Associate Dean, in the College of Education. As part of this project, Pillen provides mathematical content and works to increase the teachers’ understanding of important ideas in mathematics. The experience, Pillen says, is not a one-way street; indeed, “The teachers teach me how to teach. I enjoy it a great deal.” In the assessment-driven world of education, Pillen says “we should trust our teachers.” Pillen credits his wife, Dr. Elena Galaktionova, for inspiring him to get involved in the Teacher Circle. The Mobile Math Teacher Circle came into existence after Galaktionova obtained an invitation for a local team —made of two middle school teachers plus their principal— to attend a workshop on Teacher Circles at the American Institute of Mathematics in Palo Alto, California.

When not engrossed in teaching and research, Pillen loves to play and to watch soccer. Other hobbies include camping, hiking, and canoeing, as well as spending time with colleagues each Friday during the “Happy Hour” at the Mellow Mushroom.