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John Meier, associate professor of mathematics, is one of just two people in the nation to receive a prestigious 2003 Centennial Fellowship from the American Mathematical Society.
The primary selection criterion for the Centennial Fellowship is excellence of the candidate’s research.
The grant will support an upcoming yearlong research project by Meier on topology at Columbia University and the University of California-Santa Barbara. Topology is a field concerned with the search for “immutable properties” – those preserved under continuous transformations – and has applications in disciplines such as physics and economics.
Recipient of Lafayette’s Jones Faculty Lecture and Student Government Teaching Awards, Meier involves Lafayette students in his research. He has coauthored six papers with students and advised others in year-long honors research projects.
One of his students in an upper-level geometry course, Kevin Penderghest ’05, a mathematics major from Lindenwold, N.J., gave a presentation in February on an unsolved problem in geometry before an audience of about 70 at the Regional Student Mathematical Conference hosted by Moravian College. The presentation drew many questions from the interested group of mathematicians.
“John is a very dedicated teacher and a really nice guy,” says Penderghest. “I enjoyed his class because he explains things very well and always is willing to devote his free time to you if you are having trouble with something.”
Meier also advises student research groups in the National Science Foundation’s Research Experience for Undergraduates summer program hosted by Lafayette. Last year, Lafayette students Robert McEwen ’06 of Morgantown, Pa., and Prince Chidyagwai ’05 of Marondera, Zimbabwe, joined REU peers from University of California-Berkeley, Emory University, Princeton University, Trinity University, Carnegie Melon University, Hendrix College, Davidson College, and Humboldt State University (see related story). Since 1994, Meier has coauthored five published papers with REU participants.
Meier will present research next month at the Cornell Topology Festival.
“One thinks of polynomials like y = x^2 as algebraic objects,” he explains. “Yet early on we learn that you can understand y=x^2 by studying its graph, a parabola. So you can gain intuition for algebra by looking at associated geometric objects. The algebraic objects I study are called ‘groups,’ and I try to find useful geometric objects that tell me something about these groups.”
The field of topology has an interesting history, adds Meier.
“Mathematicians originally studied groups because they encode information about symmetry,” he says. “Given any geometric object — a cube, for example, or a frieze pattern decorating a wall — you can talk about all the symmetries of that object. This set of symmetries is called the ‘group of symmetries.’ Eventually, mathematicians started studying purely formal, algebraic objects called ‘groups’ that act like a collection of symmetries, but aren’t presented as such. What I try to do is to take a formal, abstract group G and find a geometric object whose group of symmetries is G. This is made particularly difficult as the groups I look at have infinitely many elements, hence the objects I make have to be infinitely big.”
Meier is co-author of Writing in the Teaching and Learning of Mathematics, a book on the use of writing as a pedagogical tool in mathematics, published by Mathematical Association of America. He has also shared his research through many articles in scholarly journals and conferences in his field. He is an active reviewer for Mathematical Review and has refereed papers for several mathematics journals and the pedagogical journal PRIMUS. He also has organized workshops and seminars, including the current Lafayette/Lehigh Geometry/Topology Seminar.
Since 1999, Meier has served as a consultant for Project NExT (New Experiences in Teaching), a program for new or recent Ph.D.s in mathematical sciences who are interested in improving the teaching and learning of undergraduate mathematics. He has been a member of the Executive Committee of the Eastern Pennsylvania and Delaware section of the Mathematical Association of America since 2001.
Meier joined the Lafayette faculty in 1992. His primary specialty is geometric group theory. His teaching areas include calculus, geometry, linear algebra, and real analysis.
“My work is somewhere near the intersection of algebra, geometry, and topology,” he says. “This makes it an exciting place to look for results as I get to use tools from lots of different areas to find theorems of interest to many different areas.”
Meier also has taught a seminar called Counting and Culture in Lafayette’s Values and Science/Technology (VAST) program, exploring connections between math and culture, especially in traditional African cultures and pre-Columbian civilizations.
A native of Casper, Wyo., Meier holds master’s and doctoral degrees in math from Cornell University and a B.A. in math from University of Virginia.