Symplectic geometry, physics and algebraic combinatorics

辛几何、物理学和代数组合学

• 批准号: 0093647
• 负责人: Christopher Woodward
• 金额: --
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-08-01 至 2007-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0093647&HistoricalAwards=false
• 关键词: Symplectic; geometry; physics; algebraic; combinatorics

AbstractAward: DMS-0093647Principal Investigator: Christopher T. WoodwardThe principal investigator plans to develop the theory of groupactions on symplectic manifolds and geometric invariant theory,and extend applications to certain 2d conformal field theoriesand algebraic combinatorics. In particular, he will investigatethe theory of loop group actions, group-valued moment maps, andrelations to the Wess-Zumino-Witten model in conformal fieldtheory and cohomology pairings on moduli spaces of flatconnections; the asymptotic limit of the quantum 6j symbols; anddecomposition of products of conjugacy classes in disconnectedcompact groups and twisted forms of quantum cohomology. He willintegrate his research with a variety of educational projects,such as dynamical systems in the calculus and linear algebrasequence at Rutgers; strengthening the joint major with computerscience; laboratory activities in the undergraduate curriculumand evaluation of their effectiveness.Symplectic geometry is the mathematical framework for the studyof classical mechanics, and in particular Hamiltonian dynamicalsystems. Woodward will undertake a number of projects to developthe field and its role in the undergraduate and graduatecurriculum. He will seek to understand symmetries, especially ofinfinite dimension, in this setting. Possible applicationsoutside of mathematics are the development of new computationaltechniques in conformal field theory, an important topic inrecent high-energy theoretical physics, and improvement of theefficiency of wireless communication, via the construction ofbetter packings in the unitary group.

摘要奖：DMS-0093647主要研究者：Christopher T.主要研究者计划发展辛流形上的群作用理论和几何不变理论，并将应用扩展到某些二维共形场理论和代数组合学。 特别是，他将investigatethe理论的循环组行动，组值的时刻地图，和关系到Wess-Zumino-维滕模型在共形场论和上同调配对模空间的flatconnections;的渐近极限的量子6 j符号; anddecomposition产品的共轭类disconnectedcompact组和扭曲形式的量子上同调。 他将把他的研究与各种教育项目结合起来，如罗格斯大学的微积分和线性代数序列中的动力系统;加强与计算机科学的联合专业;本科生的实验室活动及其有效性的评估。辛几何是经典力学研究的数学框架，特别是哈密顿动力系统。 伍德沃德将承担一些项目，以发展该领域及其在本科和研究生课程中的作用。 他将寻求理解对称性，特别是有限维，在这种情况下。 可能的数学以外的应用是共形场论中新的计算技术的发展，这是最近高能理论物理中的一个重要课题，以及通过在酉群中构造更好的填充来提高无线通信的效率。