CBMS Conference: Tensors and Their Uses in Approximation Theory, Quantum Information Theory, and Geometry

CBMS 会议：张量及其在逼近论、量子信息论和几何中的应用

• 批准号: 1642659
• 负责人: Luke Oeding
• 金额: $ 3.53万
• 依托单位: Auburn University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2017
• 资助国家: 美国
• 起止时间: 2017-04-01 至 2018-03-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1642659&HistoricalAwards=false
• 关键词: CBMS; Conference; Tensors; Their; Uses

This award supports a 5-day CBMS conference on "Tensors and their uses in approximation theory, quantum information theory, and geometry," at Auburn University, Auburn, AL, July 24-28, 2017. The theme is centered on uses of tensors in approximation theory, quantum information theory and other areas from a geometric perspective. The conference features Dr. J.M. Landsberg of Texas A&M University, a leading expert in the algebraic and geometric study of tensors and their applications, who will deliver 10 lectures and produce a monograph to be published in the CBMS series and will provide a much-needed resource, enabling researchers who use tensors to develop the new thinking and perspectives that underlie the theory of tensors. The award will support a diverse group of 7 discussion leaders and 25 junior researchers from the southeastern region of the US. Women, underrepresented minorities, graduate students, post-doctoral associates, junior faculty, and faculty at primarily undergraduate institutions will be specifically recruited to participate. Being in the Southeast, Auburn University is a great location to recruit from a diverse population. The conference and subsequent monograph will make connections between different areas of science and mathematics. The discussion leaders come from diverse scientific backgrounds (Algebraic Geometry, Numerical Analysis, Applied Mathematics, and Physics), so their participation will help establish cross-disciplinary communication and research. The activity will impact human resource development by enhancing the research backgrounds of participants and introducing them to open problems related to tensors. The dates (July 24-28, 2017) are set to precede the SIAM meeting on Applied Algebraic Geometry to be held in Atlanta, GA, July 31-August 4, 2017, increasing synergetic activities. This activity will lift the level of research in the southeastern region of the US.Tensors are growing in importance in all areas of science. In coordinates, a tensor is just a higher dimensional matrix. Just as in linear algebra, where we view matrices as representing linear maps in coordinates, in multi-linear algebra, i.e., the study of tensors, we view a higher dimensional matrix as representing a multi-linear map. The perspective of linear maps facilitates the study of eigenvalues and other properties independent of coordinates in linear algebra, and the perspective of multi-linear maps similarly enables the study of coordinate-independent properties of tensors. Unlike the case of linear algebra, multi-linear algebra is still in its infancy and basic questions (e.g., how to detect the rank of a multi-linear map) are open and subtle. The main goal of the proposed conference is to introduce a large group of individuals to the state of the art in theory and recent important applications. More specifically, the lectures' aims are: To give an elementary introduction to tensors, their geometry and uses accessible to beginning graduate students. To describe applications that have either not been treated in expository form previously, or had been treated from a completely different perspective (e.g., of physics or numerical analysis rather than a geometric perspective). To describe recent breakthroughs in the study of tensor rank and border rank. To bring attention to open questions--both old and recent--regarding tensors. Graduate students and young researchers will become equipped to start on open problems, allowing them to begin contributing to scientific discovery right away.Conference website: http://www.auburn.edu/~lao0004/cbms.html

该奖项支持了为期5天的CBMS会议，上面是“张量及其在近似理论，量子信息理论和几何学中的用途”，在2017年7月24日至28日在阿拉巴马州奥本的奥本大学举行。该主题以近似值理论，量子信息理论的用途为中心，量子信息理论和其他领域的用途。 The conference features Dr. J.M. Landsberg of Texas A&M University, a leading expert in the algebraic and geometric study of tensors and their applications, who will deliver 10 lectures and produce a monograph to be published in the CBMS series and will provide a much-needed resource, enabling researchers who use tensors to develop the new thinking and perspectives that underlie the theory of tensors.该奖项将支持来自美国东南部地区的7个讨论领导人和25名初级研究人员组成的多样化小组。 妇女，代表性不足的少数族裔，研究生，博士后同事，初级教职员工和教师将专门招募本科机构。奥本大学在东南部，是从不同人口招募的好地方。会议和随后的专着将在科学和数学的不同领域之间建立联系。讨论领导者来自多种科学背景（代数几何，数值分析，应用数学和物理学），因此他们的参与将有助于建立跨学科的交流和研究。这项活动将通过增强参与者的研究背景并将其引入与张量有关的问题来影响人力资源的开发。日期（2017年7月24日至28日）定于2017年7月31日至8月4日在佐治亚州亚特兰大举行的SIAM会议之前，将在佐治亚州亚特兰大举行，以增加协同活动。这项活动将提高美国东南部地区的研究水平。在所有科学领域，观察者都在重要性。在坐标中，张量只是一个较高的维矩阵。就像在线性代数中一样，我们将矩阵视为代表坐标中的线性图，在多线性代数中，即对张量的研究，我们将较高的维矩阵视为代表多线性图的较高维矩阵。线性图的观点促进了独立于线性代数中坐标的特征值和其他特性的研究，多线性地图的观点类似地可以研究启动器的坐标非依赖性特性。与线性代数不同，多线性代数仍处于起步阶段和基本问题（例如，如何检测多线性图的等级）是开放且微妙的。拟议会议的主要目标是在理论上和最新的重要应用中向一大群人介绍最新的现状。 更具体地说，讲座的目的是：对张量，其几何形状进行基础介绍，并用来访问初学者。描述以前尚未以说明性形式处理过的应用，或者是从完全不同的角度（例如物理学或数值分析而不是几何观点）处理的。描述张量排名和边界等级的研究中的最新突破。为了引起人们的关注 - 最近和最近的张力张量。研究生和年轻的研究人员将有能力从开放问题开始，使他们能够立即开始为科学发现做出贡献。会议网站：http：//www.auburn.edu/~lao 0004/cbms.html