Symplectic geometry, physics and algebraic combinatorics

摘要奖：DMS-0093647主要研究人员：Christopher T.Woodward主要研究人员计划发展辛流形上的群作用理论和几何不变量理论，并将其应用扩展到某些二维共形场理论和代数组合学。特别是，他将研究循环群作用的理论，群值矩映射，以及与共形场论中的Wess-Zumino-Witten模型的关系，以及平坦连通的模空间上的上同调对；量子6J符号的渐近极限；以及不连通紧群中共轭类的乘积的分解和量子上同调的扭曲形式。他将把他的研究与各种教育项目结合起来，例如罗格斯大学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；本科课程中的实验室活动及其有效性的评估。辛几何是研究经典力学，特别是哈密尔顿动力学系统的数学框架。伍德沃德将承担一些项目，以发展该领域及其在本科生和研究生课程中的作用。他将试图在这种背景下理解对称性，特别是无限维的对称性。数学之外的可能应用是发展共形场理论中的新计算技术，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包装来提高无线通信的效率。

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.