PECASE: Determinants of Elliptic and Toeplitz Operators withApplications to Geometry

9703329 Okikiolu本奖项支持的研究属于几何分析的一般领域。更具体地说，研究者是研究闭紧黎曼流形上的拉普拉斯行列式在度规中所有使总体积固定的光滑扰动下的性质。这可能会对庞加莱猜想产生影响。此外，研究者将考虑一般负弯曲流形上的波算符与量子混沌理论的联系。该奖项是在教师早期职业发展（Career）计划下颁发的，该计划资助包含高度有价值的研究以及强大的教育成分的项目。例如，该奖项的研究人员打算为学生举办夏季研讨会，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，为市中心的教室描绘模范课程，帮助开发市中心K-12数学和科学课程。课程将包括直接导致数学研究的设计和建造活动，并纳入少数民族社会文化的元素。

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.