9703329 Okikiolu The research supported in this award lies in the general area of geometric analysis. More specifically, the investigator is to study properties of the determinant of the Laplacian on closed compact Riemannian manifolds under all smooth perturbations in the metric which leave the total volume fixed. This may have implications for the Poincare conjecture. In addition, the investigator is to consider the wave operator on general negatively curved manifolds in connection with quantum chaos theory. This award is made under the Faculty Early Career Development (CAREER) program which funds projects that contain highly meritorious research coupled with a strong educational component. For example, the investigator of this award intends to run summer workshops for students introducing them to various current problems in geometric analysis using numerical methods. Also, she is to help develop inner-city K-12 mathematics and science curricula by producing a series of videos depicting model lessons for the inner-city classroom. The lessons will involve design and construction activities which lead directly to the study of mathematics, and incorporate elements from minority social cultures.
