A Research Experiences for Undergraduates site supporting eight students will be funded by this grant. The focus of the research will change over the three-year grant duration, with the first group concentrating on (1) planar domains which grow along the gradient of the Green's function, a phenomenon related to symmetry breaking in needle crystal growth, (2) on local zeta functions over p-adic fields where (symbolic) computation of examples is of primary importance and (3) on the topology of real critical points in which one seeks to analyze critical points of perturbations of polynomials with isolated critical points. Students will work as teams on projects which combine extensive computer experimentation with mainstream mathematics or statistics issues. In addition to weekly student presentations, exchanges with other REU sites will be scheduled. There will also be regular visits made to the NSF Regional Geometry Institute at Amherst College. Teams will produce final reports and manuscripts for publication where suitable. All students will be encouraged to present the results of their work at professional meetings or at their home institutions.
