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.

0853000OEDINGINGINGING这项奖项是根据2009年的《美国复苏与再投资法》（公法111-5）资助的。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9到二十四个月的研究。 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在其工作中的张力空间中发生的品种，例如统计数据（依赖关系研究），计算复杂性理论（通过张量的等级来界定算法的复杂性）和物理学（量子信息理论和纠缠的量子理论）。这项研究的重点是解决有关P. Comon（美国索菲亚 - 安提波利的U. Nice，电气工程）提出的有关张量和对称张量的问题的问题，以及有关L. de Lathauwer（K.U.Leuuven，Electrical Engineering，Electrical Engineering）提出的有关张量的块分解的问题。这些基本信息将通过分析被称为Secant品种的经典几何对象找到。该项目的目标是以几何语言来重述，是找到Segre-veronese品种和子空间品种的Secant品种的新方程。通过从经典代数几何学和表示理论的角度研究这些问题，可以使用许多古典和最新技术。拟议的研究将结合理论和计算技术，以研究PI在PI的论文中使用和开发的G型与主持人科学家在经典代数几何学方面的专业知识，以解决信号处理中的问题，并进一步在几何学和代表方面进行PI研究。该项目将通过培养国际和跨学科的社会来影响社会，以促进国际和跨学科的社会，并培养工程师和跨学科的协作。这项研究的发现还将使统计，计算复杂性和物理学等领域受益。