SM: Conference on Symmetry in Mathematics and Physics

摘要奖：DMS-0753874主要研究者：Donald Babeland，Srinivasa R.会议的主题将是重要的最新成果和突出的问题领域的表示理论的有限和无限维李群和超级李群，及其应用到量子计算，几何，物理和微分方程，不同的领域被统一下的过度主题的对称性表现在几何行动的群体和他们的代表。演讲者将是这些领域的国际公认的研究人员，观众预计将是这些领域的高级研究人员，高级研究生，博士后和初级教师的混合体，他们渴望或已经在这些领域做出重要贡献。将为后一组的选定参与者提供旅费，特别重视妇女和代表人数不足的少数群体。应该指出的是，12名发言者中有4名是妇女。会议的背景包括由物理学家如祖米诺和费拉拉（都是会议的发言人）开创的超对称性工作，以及数学家卡茨、穆迪和其他关注无限维李代数及其在量子场论中的应用的人的工作。在20世纪90年代，群论的观点被成功地应用于亚纯微分方程及其模的理论。最近，超对称性理论的发展及其在超粒子分类中的应用，差分方程的微分伽罗瓦群理论的研究，以及超几何基础的研究都取得了重要的新进展。对称性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，比如为什么氢和氧联合收割机会产生水。对称性的一个例子是：考虑一个普通的正方形，用金属丝做成，绕中心旋转90度，注意它又回到了自己的位置上，尽管金属丝的分子已经移动了。再做一次，你仍然得到相同的平方。当你第四次做的时候，你把它旋转360度，金属丝的分子就会回到它们开始的地方。在代数语言中，这表示4阶循环群是正方形的对称群。令人惊奇的是，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。在这次会议上要考虑的对称性是同一个故事的一部分。也许特别感兴趣的是用于亚粒子物理学研究的超对称性理论概念。这个概念的创始人，B。祖米诺将在这次会议上发言。目前这是一个理论假设，许多人相信是正确的，但等待实验验证。位于日内瓦的欧洲核子研究中心（CERN）的主要目标之一是利用其价值数十亿美元的强子对撞机（2008年投入使用）在实验上建立超对称性假说。 欲了解更多信息，请访问会议网站www.math.ucla.edu/symmetry。该奖项由几何分析、概率论、代数、数论和组合数学项目共同资助。

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.