International Research Fellowship Program: Secant Varieties and Applications to Signal Processing

国际研究奖学金计划：割线品种及其在信号处理中的应用

• 批准号: 0853000
• 负责人: Luke Oeding
• 金额: $ 16.68万
• 依托单位: Oeding Luke A
• 依托单位国家: 美国
• 项目类别: Fellowship Award
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-06-01 至 2011-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0853000&HistoricalAwards=false
• 关键词: International; Research; Fellowship; Program; Secant

0853000OedingThis award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).The International Research Fellowship Program enables U.S. scientists and engineers to conduct nine to twenty-four months of research abroad. The program's awards provide opportunities for joint research, and the use of unique or complementary facilities, expertise and experimental conditions abroad.This award will support a twenty-four-month research fellowship by Dr. Luke Oeding to work with Dr. Girogio Ottaviani at Universita degli Studi di Firenze in Italy.The primary goal of this project is to provide fundamental information to engineers in signal processing and to researchers in other disciplines that use varieties occurring in spaces of tensors in their work such as statistics (the study of dependence relations), computational complexity theory (bounding the complexity of algorithms via ranks of tensors) and physics (quantum information theory and measures of entanglement). The research is focused on solving questions about the decomposition of tensors and symmetric tensors posed by P. Comon (U. Nice at Sophia-Antipolis, electrical engineering) and questions about block decomposition of tensors posed by L. De Lathauwer (K.U.Leuven, electrical engineering). This fundamental information will be found via analyzing classical geometric objects known as secant varieties. Restated in geometric language, the goal of this project is to find new equations of secant varieties of Segre-Veronese varieties and secant varieties of subspace varieties. By studying these questions from the standpoint of classical algebraic geometry and representation theory, many classical and recent techniques can be used. The proposed research will combine theoretical and computational techniques for studying G-varieties used and developed in the PI's dissertation with the host scientist's expertise in classical algebraic geometry to solve questions in signal processing and further the PI's research in geometry and representation theory.This project will impact society by fostering international and cross-disciplinary collaboration between engineers and mathematicians. The findings of this research will also benefit areas such as statistics, computational complexity, and physics.

0853000Oeding 该奖项根据 2009 年美国复苏和再投资法案（公法 111-5）提供资金。国际研究奖学金计划使美国科学家和工程师能够在国外进行九到二十四个月的研究。 该项目的奖项为联合研究以及使用国外独特或互补的设施、专业知识和实验条件提供了机会。该奖项将支持 Luke Oeding 博士与意大利佛罗伦萨大学的 Girogio Ottaviani 博士合作为期 24 个月的研究奖学金。该项目的主要目标是为信号处理工程师和使用其他学科的研究人员提供基础信息。 他们的工作中出现了张量空间中的各种变化，例如统计学（依赖关系的研究）、计算复杂性理论（通过张量的等级限制算法的复杂性）和物理学（量子信息理论和纠缠测量）。该研究的重点是解决 P. Comon（U. Nice at Sophia-Antipolis，电气工程）提出的有关张量和对称张量分解的问题以及 L. De Lathauwer（K.U.Leuven，电气工程）提出的有关张量分块分解的问题。通过分析称为割线簇的经典几何对象可以找到这一基本信息。用几何语言重述，该项目的目标是找到塞格雷-维罗内塞簇的割线簇和子空间簇的割线簇的新方程。通过从经典代数几何和表示论的角度研究这些问题，可以使用许多经典和最新的技术。拟议的研究将把研究 PI 论文中使用和开发的 G 簇的理论和计算技术与宿主科学家在经典代数几何方面的专业知识相结合，以解决信号处理中的问题，并进一步推进 PI 在几何和表示理论方面的研究。该项目将通过促进工程师和数学家之间的国际和跨学科合作来影响社会。这项研究的结果还将有益于统计学、计算复杂性和物理学等领域。