Support for eight undergraduate students is provided by this Research Experiences for Undergraduates award. The award continues an earlier program of research in applied and discrete mathematics, matroid theory and mathematical modeling. Students will work in small teams under faculty advisors. Written reports at the end of the program are required. Where possible, students will be encouraged to rewrite the reports for publication and presentation at professional meetings. Research projects include studies on birigid graphs in the plane and their excess (the number of edges which can be discarded without destroying rigidity). The problem to be taken up concerns the existence of minimal birigid graphs with arbitrary excess. Combinatorial characterizations of birigid graphs in higher dimensions will also considered. Work will be done on bifurcation problems in autocatalytic chemical reactions. These reactions are prime examples of nonlinear systems whose modeling (reaction diffusion equations) are not well understood. The objective of this project will be to determine the symmetry properties of the system, the bifurcation diagram and the properties of its solutions. Symbolic and numerical computations are expected to play an important role in much of the research to be done.
