IMA SUMMER SCHOOL ON MODERN APPLICATIONS OF REPRESENTATION THEORY (SUPPLEMENTARY FUNDING), July 20 - August 6, 2014

IMA 表征理论现代应用暑期学校（补充经费），2014 年 7 月 20 日至 8 月 6 日

• 批准号: 1642608
• 负责人: Imre Kondor
• 金额: $ 2.47万
• 依托单位: Pennsylvania State Univ University Park
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-12-01 至 2017-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1642608&HistoricalAwards=false
• 关键词: IMA; SUMMER; MODERN; APPLICATIONS; REPRESENTATION

A three-week long summer school for graduate students in "Modern Applications of Representation Theory" will take place at the University of Chicago from July 20 to August 6, 2014 as part of the Institute for Mathematics and Applications (IMA) Graduate Students Summer Programs. In mathematics symmetries are described by abstract objects called groups. Representation theory, originating in the work of mathematicians such as Issai Schur and Ferdinand Frobenius at the end of the 19th century, studies how the structure of groups can be captured by simpler, linear objects, in particular, matrices. Apart from making groups more concrete, it has long been realized that this is critical for understanding how groups act on other objects. For example, in physics one is interested in how the symmetry groups of nature, such as translations and rotations, act on physical systems. This is why, starting in the 1920's, the representation theory of unitary groups, in particular, has been central to the development of quantum mechanics and particle physics. Recently, surprising connections have also been uncovered between representation theory and problems of a seemingly very different character, such as finding the number of operations required on a computer to carry out arithmetic computations, aligning a large number of noisy images of the same molecule taken by a certain type of electron-microscope, and ranking problems in statistical machine learning. The aim of the summer school is to engage graduate students from across the sciences in research in these exciting new areas.In recent years representation theory has found new applications in a range of domains from cryo-electron microscopy, through machine learning, to holographic algorithms. The fact that the subject is usually taught for an audience in pure mathematics makes it challenging for graduate students in more applied disciplines to learn the material. Conversely, mathematicians are often not aware of the new, exciting applications of representation theory. This summer school attempts to bridge this gap by starting with a short introduction to representation theory, followed by a series of mini-courses on some of the most recent work on using representation theoretical ideas in imaging, signal processing, holographic algorithms, quantum computing, algebraic and geometric computational complexity theory, non-commutative Fourier transforms, and other areas. Each of these subjects is presented by one of the leading experts in the area. The website for the summer school can be found here: www.ima.umn.edu/event/index.php?event_id=PISG7.20-8.6.14

2014年7月20日至8月6日，将在芝加哥大学（University of Chicago）举行三周的暑期学校，旨在在芝加哥大学进行“现代应用理论”的研究生，这是数学与应用程序研究所（IMA）研究生暑期课程的一部分。 在数学中，对称性用称为组的抽象对象描述。 代表理论起源于19世纪末的数学家（例如Issai Schur和Ferdinand Frobenius）的工作，研究了如何通过更简单的线性对象（尤其是矩阵）捕获群体的结构。 除了使小组更具体外，长期以来已经意识到，这对于理解群体如何对其他物体的作用至关重要。 例如，在物理学中，人们对自然对称群体（例如翻译和旋转）如何作用于物理系统感兴趣。 这就是为什么从1920年代开始，尤其是统一群体的表示理论是量子力学和粒子物理学发展的核心。 最近，在表示理论和看似非常不同的特征的问题之间也发现了令人惊讶的连接，例如找到计算机上所需的操作数量以进行算术计算，使一定类型的电子 - 微镜拍摄的相同分子的大量噪声图像与统计机器学习中的一定类型的分子相符。 暑期学校的目的是在这些令人兴奋的新领域的研究中吸引来自整个科学的研究生。代表理论在从冷冻电子显微镜，通过机器学习到全息算法的一系列领域中发现了新的应用。 通常为纯粹数学的观众教授该主题的事实使得对更多应用学科的研究生在学习材料方面具有挑战性。相反，数学家通常不了解代表理论的新的，令人兴奋的应用。 今年暑期学校试图通过简短的表示理论介绍来弥合这一差距，然后在一些有关在成像，信号处理，全息算法，量子计算，代数和几何计算复杂性理论，非公认傅立叶变换和其他区域中使用代表理论思想的最新工作中进行了一系列迷你表演。 这些主题中的每一个都是由该地区的一位领先专家提出的。 可以在此处找到暑期学校的网站：www.ima.umn.edu/event/index.php?event_id=pisg7.20-8.6.14