Research on Lensless Microscopy

无透镜显微镜研究

• 批准号: 9460231
• 负责人: Kendall Preston
• 金额: $ 6.13万
• 依托单位: Kensal Corporation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-06-15 至 1996-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9460231&HistoricalAwards=false
• 关键词: Research; Lensless; Microscopy

This award supports the research of Professor P. Aluffi to work in algebraic geometry. He will work on problems deriving from the study of hypersurface singularities. He hopes to find a new formula for MacPherson's Chern class and to extend results on duality of projective varieties. He hopes to apply some of these results to the study of combinatorial questions on graphs. The research is in the field of algebraic geometry, one of the oldest parts of modern mathematics, but one which blossomed to the point where it has, in the past 10 years, solved problems that have stood for centuries. Originally, it treated figures defined in the plane by the simplest of equations, namely polynomials. Today, the field uses methods not only from algebra, but also from analysis and topology, and conversely it is extensively used in those fields. Moreover it has proved itself useful in fields as diverse as physics, theoretical computer science, cryptography, coding theory and robotics.

该奖项支持P.Aluffi教授致力于代数几何的研究。他将致力于研究超曲面奇点所衍生的问题。他希望为MacFherson的Chern类找到一个新的公式，并推广关于射影簇的对偶的结果。他希望将这些结果中的一些应用于图上的组合问题的研究。这项研究是在代数几何领域进行的，代数几何是现代数学中最古老的部分之一，但在过去的10年里，它发展到了解决了几个世纪以来的问题的地步。最初，它用最简单的方程，即多项式来处理平面上定义的图形。今天，这个领域不仅使用代数的方法，而且还使用分析和拓扑学的方法，相反，它在这些领域被广泛使用。此外，它在物理、理论计算机科学、密码学、编码理论和机器人学等领域都证明了自己的有用。