SM: Conference on Symmetry in Mathematics and Physics

项目编号：dms -0753874会议的主题将是有限维和无限维李群和超李群的表示理论领域的重要最新成果和突出问题，及其在量子计算、几何、物理和微分方程中的应用，不同的领域被统一在对称的首要主题下，表现在几何群的行为及其表示。演讲者将是这些领域的国际知名研究人员，听众预计将是这些领域的高级研究人员，以及渴望或已经在这些领域做出重要贡献的高级研究生，博士后和初级教师。将向后一组的选定参加者提供旅费，特别强调妇女和代表性不足的少数民族。应该指出，12位发言人中有4位是女性。会议的背景包括由物理学家如祖米诺和费拉拉（他们都在会议上发言）开创的关于超对称的工作，以及数学家卡茨、穆迪等人的工作，他们把重点放在了无限维李代数及其在量子场论中的应用上。20世纪90年代，群论观点成功地应用于亚纯微分方程及其模的理论。最近，超对称麦基理论的发展及其在超粒子分类中的应用，微分伽罗瓦差分方程群论的研究，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，例如为什么氢和氧结合成水。对称的一个例子如下：考虑一个用金属丝做成的普通正方形，绕其中心旋转90度，注意到尽管金属丝的分子移动了，但它还是回到了原来的位置。再做一次，你还是得到同样的正方形。当你做第四次的时候，也就是，把它旋转360度，导线上的分子就会回到开始的地方。用数学语言来说，这表示&amp；#147；4阶环群；是正方形的对称群。对称和群的概念可以扩展和丰富，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，这是一个奇迹。本次会议将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用于研究亚粒子物理的超对称理论概念。这一概念的创始人B. Zumino将在本次会议上发言。目前这是一个理论假设，许多人认为是正确的，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2008年投入使用的价值数十亿美元的强子对撞机，通过实验建立超对称假说。欲了解更多信息，请参阅会议网站www.math.ucla.edu/symmetry。该奖项由几何分析、概率论、代数、数论和组合学项目联合资助。

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.