PECASE: Determinants of Elliptic and Toeplitz Operators withApplications to Geometry

9703329 Okikiolu该奖项所支持的研究涉及几何分析的一般领域。更具体地说，研究闭紧黎曼流形上拉普拉斯行列式在度量中的所有光滑扰动下的性质。这可能会对庞加莱猜想产生影响。此外，本文还结合量子混沌理论，研究了一般负曲流形上的波算符。该奖项是根据教师早期职业发展(Career)计划颁发的，该计划为包含高度有价值的研究和强大的教育成分的项目提供资金。例如，该奖项的调查者打算为学生举办暑期工作坊，向他们介绍使用数值方法进行几何分析的各种当前问题。此外，她还将通过制作一系列视频来帮助开发市中心的K-12数学和科学课程，这些视频描绘了市中心课堂上的示范课程。课程将涉及设计和建造活动，这些活动直接导致数学学习，并纳入少数群体社会文化的元素。

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.