Focused Research Group: Calabi-Yau Manifolds and their Applications

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AbstractAward: DMS-0074177Principal Investigator: Michael R. DouglasThis 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, and NSF funds are supporting thisinterdisciplinary group's collaborations throughvideoconferencing and travel.