SM: Conference on Symmetry in Mathematics and Physics

SM：数学和物理对称性会议

• 批准号: 0753874
• 负责人: Donald Babbitt
• 金额: --
• 依托单位: University of California-Los Angeles
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-04-15 至 2010-03-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0753874&HistoricalAwards=false
• 关键词: SM; Conference; Symmetry; Mathematics; Physics

AbstractAward: DMS-0753874Principal Investigator: Donald Babbitt, Srinivasa R. VaradhanThe main theme of the conference will be important recent resultsand outstanding problems in the fields of representation theoryof finite and infinite dimensional Lie and super-Lie groups, andits applications to quantum computing, geometry, physics, anddifferential equations, the different areas being unified underthe over-arching theme of symmetry manifested in geometricactions of groups and their representations. The speakers will beinternationally recognized researchers in these fields and theaudience is expected to be a mixture of senior researchers inthese fields together with advanced graduate students, postdocsand junior faculty who aspire to make or already are makingimportant contributions to these fields. There will be travelfunds made available to select participants of the latter groupwith a special emphasis on women and underrepresentedminorities. It should be pointed out that four of the twelvespeakers are women. The background to the conference consists ofthe work on supersymmetry pioneered by the physicists such asZumino, and Ferrara (both speakers at the conference), and thework of the mathematicians Kac, Moody, and others who broughtfocus to infinite dimensional Lie algebras and their applicationsto quantum field theory. In the 1990's the group theoretic pointof view was applied successfully to the theory of meromorphicdifferential equations and their moduli. Very recently importantnew progress has been made by the development of a supersymmetricMackey theory and its applications to super particleclassification, by work on differential Galois group theory ofdifference equations, and by the work on the foundations ofsuper-geometry.Symmetry is one of the most fundamental and useful notions inboth mathematics and theoretical physics. For example it explainsthe mysteries of the periodic table of chemical elements such aswhy hydrogen and oxygen combine to make water. An example ofsymmetry is the following; consider an ordinary square made withwire, rotate it 90 degrees about its center and notice it comesback onto itself although the molecules of the wire havemoved. Do it again, you still get the same square. When you do itthe fourth time, i.e., you rotate it 360 degrees the molecules ofthe wire come back to where they started. In mathematicallanguage this says that “the cyclic group of order 4” isthe symmetry group of the square. It is a wonder that the notionof symmetry and group can be extended and enriched to explaincomplicated sub-atomic physical phenomena as well as solvefundamental problems in mathematics coming from areas such ascryptography. The symmetries to be considered in this conferenceare part of this same story. Of perhaps particular interest isthe theoretical notion of supersymmetry used in the study ofsub-particle physics. The founder of this notion, B. Zumino, willspeak at this conference. It is presently a theoreticalhypothesis that many believe to be true but which awaitsexperimental verification. It is one of the main goals at theEuropean Center for Nuclear Research (CERN) in Geneva to use itsmulti-billion dollar Hadron Collider which comes on line in 2008to experimentally establish the supersymmetry hypothesis. Formore information see the conference Website,www.math.ucla.edu/symmetry. This award is funded jointly by theprograms in Geometric Analysis, Probability, and Algebra, NumberTheory, and Combinatorics.

摘要奖：DMS-0753874主要研究人员：斯里尼瓦萨·R·瓦拉德汉·唐纳德·巴比特会议的主题将是有限和无限维李和超李群的表示理论及其在量子计算、几何、物理和微分方程中的应用领域的重要最新结果和突出问题，不同的领域统一在对称的总体主题下，表现为群及其表示的几何行为。演讲者将是这些领域的国际公认的研究人员，听众预计将是这些领域的高级研究人员以及渴望对这些领域做出或已经做出重要贡献的高级研究生、博士后和初级教员的混合体。将向选定的后一类参与者提供旅费，特别强调妇女和代表性不足的少数群体。应该指出的是，12名运动员中有4名是女性。会议的背景包括由物理学家如Zumino和Ferrara(两人都在会议上发言)开创的超对称性工作，以及数学家Kac、Moody和其他人的工作，他们将重点放在无限维李代数及其在量子场论中的应用上。20世纪90年代，S将群论的观点成功地应用于亚纯微分方程组及其模的理论。最近，通过发展超对称Mackey理论及其在超粒子分类中的应用，通过对差分方程组的微分Galois群理论的工作，以及通过对超几何基础的工作，取得了重要的新进展。对称是数学和理论物理中最基本和最有用的概念之一。例如，它解释了化学元素周期表的奥秘，比如为什么氢和氧结合成水。下面是一个对称的例子；考虑一个用金属丝制成的普通正方形，将它绕着中心旋转90度，注意到它又回到了原来的位置，尽管金属丝的分子已经移动了。再做一次，你还是会得到同样的正方形。当你第四次这样做时，也就是说，你把它旋转360度，金属丝的分子就会回到它们开始的地方。在数学语言中，这是说4阶循环群是正方形的对称群。令人惊讶的是，对称性和群的概念可以被扩展和丰富，以解释复杂的亚原子物理现象，以及解决来自密码学等领域的数学基本问题。本次会议要考虑的对称性也是这个故事的一部分。也许特别令人感兴趣的是亚粒子物理研究中使用的超对称性理论概念。这一概念的创始人B.祖米诺将在这次会议上发言。目前，这是一个理论上的假设，许多人认为这是正确的，但还有待实验验证。日内瓦的欧洲核子研究中心(CERN)的主要目标之一是使用其数十亿美元的强子对撞机来实验建立超对称假设。强子对撞机于2008年上线。欲了解更多信息，请访问会议网站www.math.ucla.edu/symsymm。该奖项由几何分析、概率和代数、数论和组合学项目共同资助。