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Chencong Bao ’11 (Shanghai, China), Kate Finlay ’11 (Merrimack, N.H.), Peter McGrath ’11 (Burtonsville, Md.), and Jorge Sawyer ’10 (Lodi, N.J.) presented research at the 2010 joint meeting of the American Mathematical Society and Mathematical Association of America in San Francisco.
Bao and McGrath presented their paper “Matroids, Geometry, Symmetry and the 4th Dimension.” Their research was part of Lafayette’s eight-week summer Research Experiences for Undergraduates (REU) math program, in which students work in small groups with a faculty mentor on unsolved mathematics problems. The team’s adviser was Gary Gordon, professor of mathematics, and included students from Claremont McKenna College and Loyola Marymount University.
“Doing research has some obvious benefits for someone interested in graduate school–learning to prepare talks and papers and so forth. But being surrounded by math students from lots of different schools has given me a wider perspective for my future,” says McGrath, who has aspirations of getting a Ph.D. in mathematics and working for a company like Microsoft or Google.
Finlay was part of another math REU team that presented research on “Complete Growth and Graph Products of Groups.” The team’s adviser was John Meier, professor of mathematics, and included students from Northwestern University, University of Maine, and Wake Forest University.
Sawyer presented advanced research he worked on with Clifford Reiter, professor of mathematics, about their discovery of a perfect parallelepiped, an object widely searched for by number theorists. A parallelepiped is a skew box. Like an ordinary box, it has parallel faces, but the angles need not be 90 degrees.
Sawyer performed searches for 2-D perfect parallelograms and developed formulas based upon a simple representation of the parallelograms. Reiter then wrote an algorithm based on Sawyer’s perfect parallelograms, and they used the formulas to sift through millions of cases. Using this method, the pair found some examples of perfect parallelepipeds. Their work also is being published in the JP Journal of Algebra and Number Theory and Applications.