St. Peter's College

Title: Ramsey Theory on Finite Groups

Director(s): Brian Hopkins

Dates of Program: May 30 - July 30, 2006

Summary: These Saint Peter's College students will be coloring elements of finite groups as efficiently as possible to avoid certain structures. For example, given a finite group G with non-identity elements x, y, z, not necessarily distinct, how many colors are necessary to avoid a "monochromatic solution" to xy = z? This question has been answered for groups of order 16 and less; we will forge on. Following recent research in Ramsey theory on the integers, related topics include working with other equations, such as xyy = z, and counting the number of distinct colorings once the minimal number of colors is known.

In addition, all five students will participate in the Undergraduate Summer School of the Park City Mathematics Institute / Institute for Advanced Study, 25 June - 15 July.