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.

0853000 Oeding该奖项是根据2009年美国复苏和再投资法案（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24个月的研究。 该计划的奖项提供了联合研究的机会，以及使用独特或互补的设施，专业知识和国外的实验条件。这个奖项将支持一个二十四-Luke Oeding博士与Girogio Ottaviani博士一起在意大利佛罗伦萨大学进行为期一个月的研究。该项目的主要目标是为信号处理工程师和其他领域的研究人员提供基础信息。在工作中使用张量空间中出现的各种各样的学科，如统计学（依赖关系的研究），计算复杂性理论（通过张量等级限制算法的复杂性）和物理学（量子信息理论和纠缠度量）。研究的重点是解决P. Comon（U。尼斯在Sophia-Antipolis，电气工程）和张量提出的块分解的问题。De Lathauwer（K.U.Leuven，电气工程）。这些基本信息将通过分析被称为割线变体的经典几何对象来发现。用几何语言重申，这个项目的目标是找到Segre-Veronese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观点研究这些问题，可以使用许多经典的和最近的技术。该研究计划将联合收割机的理论和计算技术，研究G-品种使用和开发的PI的论文与主持科学家的专业知识，在经典代数几何解决信号处理的问题，并进一步PI的研究在几何和表示理论。该项目将影响社会，促进国际和跨学科的合作之间的工程师和数学家。这项研究的结果也将有利于统计学，计算复杂性和物理学等领域。