Focused Research Group: Calabi-Yau Manifolds and their Applications

摘要奖：DMS-0074072首席研究员：大卫·R·莫里森这个研究项目汇集了三个校区的数学家和物理学家团队，共同致力于弦理论。具体的研究任务包括研究具有8个超荷的理论中的超多重模空间的量子修正、异质弦紧化的模空间的结构、在整体完整群位于例外Lie群G2的七维空间上紧凑的M理论模型、Calabi-Yaufour Folds上的M理论模型以及奇点上的膜的ADS/CFT对应的研究。弦理论是在最基本的层次上建立宇宙统一理论的一个很有前途的候选者。尽管基本思想很简单--基本粒子应该被建模为数学循环，而不是点--但解决这个理论的细节涉及并启发了一些食品化的数学工具和思想。这项任务没有人完成，即使在一个数学和物理之间的协同特别富有成效的领域，对Calabi-Yau空间的研究似乎是经典弦运动方程的解。这是授予包括杜克大学、哥伦比亚大学和罗格斯大学的数学家和物理学家的研究小组的三个相关奖项之一。该奖项的资金为杜克大学的研究人员提供核心支持，并通过视频会议和旅行支持这个跨学科小组的合作。

AbstractAward: DMS-0074072Principal Investigator: David R. MorrisonThis research project brings together a team of mathematiciansand physicists based at three campuses to work together on stringtheory. Specific research tasks include the study of the quantumcorrections to the mypermultiplet moduli spaces in theories witheight supercharges, the structure of the moduli spaces ofheterotic string compactifications, M-theory models compactifiedon seven-dimensional spaces whose global holonomy group lies inthe exceptional Lie group G2, M-theory models on Calabi-Yaufourfolds, and a study of the AdS/CFT correspondence for branesat singularities.String theory is a promising candidate for a unifying theory ofthe universe at its most fundamental levels. Although the basicidea is simple - elementary particles should be modeled asmathematical loops of stgring rather than as points - working outthe details of this theory has involved and inspired somesophisticated mathematical tools and ideas. The task is by nomeans complete, even in an area where the synergy betweenmathematics and physics has been particularly productive, thestudy of the Calabi-Yau spaces that appear as solutions of theclassical string equations of motion. This is one of threelinked awards to a research group that includes mathematiciansand physicists at Duke University, Columbia University, andRutgers University. Funds in this award provide core support forthe researchers at Duke and are supporting this interdisciplinarygroup's collaborations through videoconferencing and travel.