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

该奖项支持于 2017 年 7 月 24 日至 28 日在阿拉巴马州奥本市奥本大学举行的为期 5 天的 CBMS 会议，主题为“张量及其在逼近理论、量子信息理论和几何中的应用”。会议主题围绕张量的使用从几何角度研究近似论、量子信息论等领域。此次会议邀请了德克萨斯农工大学的 J.M. Landsberg 博士，他是张量及其应用的代数和几何研究领域的领先专家，他将发表 10 场讲座，并编写一本将在 CBMS 系列中出版的专着，并将提供急需的信息。资源，使使用张量的研究人员能够发展张量理论基础的新思维和观点。该奖项将支持来自美国东南部地区的由 7 名讨论领袖和 25 名初级研究人员组成的多元化团体。 女性、代表性不足的少数族裔、研究生、博士后、初级教师和主要本科院校的教师将被专门招募参加。奥本大学位于东南部，是从多元化人群中招募人才的绝佳地点。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。讨论领袖来自不同的科学背景（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。该活动将通过增强参与者的研究背景并向他们介绍与张量相关的开放问题来影响人力资源开发。这些日期（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 应用代数几何会议之前，以增加协同活动。这项活动将提升美国东南部地区的研究水平。张量在所有科学领域都变得越来越重要。在坐标系中，张量只是一个高维矩阵。正如在线性代数中，我们将矩阵视为表示坐标中的线性映射一样，在多线性代数（即张量的研究）中，我们将更高维的矩阵视为表示多线性映射。线性映射的视角有助于研究线性代数中与坐标无关的特征值和其他属性，而多线性映射的视角同样可以研究张量的坐标无关属性。与线性代数的情况不同，多线性代数仍处于起步阶段，基本问题（例如，如何检测多线性映射的秩）是开放且微妙的。拟议会议的主要目标是向一大群人介绍最新的理论和最新的重要应用。 更具体地说，讲座的目的是： 为研究生初级学生提供张量、其几何形状和用途的基本介绍。描述以前没有以说明形式处理过的应用程序，或者已经从完全不同的角度（例如，物理或数值分析而不是几何角度）处理过的应用程序。描述张量秩和边界秩研究的最新突破。引起人们对有关张量的开放问题（无论是旧问题还是新问题）的关注。研究生和年轻研究人员将有能力开始解决开放问题，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/~lao0004/cbms.html