Symplectic Topology (Mathematics)

麦克达夫博士将继续她对辛四维流形结构的研究。很长一段时间以来，她一直在使用J-全纯曲线的理论来尝试对它们进行分类，并在有限类流形(包含合适的2-球面的流形)中成功地做到了这一点。这种方法似乎要达到极限了。同时，Gompf等人发现了一种新的方法来构造辛4-流形的例子。麦克达夫博士建议对这种构造的可能性进行详细分析，以准确确定J-全纯曲线方法的缺陷所在。此外，她还将寻找新的辛4-流形的不变量，并通过研究最近引入辛拓扑中的新方法，如母函数，来扩大自己的知识。主办机构的互动活动包括：主持辛拓扑学新发展研讨会，并参加伯克利数学系女研究生团体诺瑟环的活动。该项目进一步推动了VPW计划的目标，即：(1)为妇女提供机会，在NSF资助的工程和科学学科中发展她们的职业生涯；(2)通过提高受雇于工业、政府和学术机构的女科学家和工程师的知名度，鼓励妇女追求科学和工程事业。通过鼓励妇女参与科学，这是对国家未来科学活力的宝贵投资。

Dr. McDuff will continue her research into the structure of symplectic 4-manifolds. For a long time she has been using the theory of J-holomorphic curves in an attempt to classify them, and has been quite successful in doing this for a restricted class of manifolds (those which contain suitable 2-spheres). The method seems to be getting to its limit. Meantime, Gompf and others have found a new way to construct examples of symplectic 4-manifolds. Dr. McDuff proposes a detailed analysis of the possibilities of this construction to determine exactly where the J-holomorphic curve methods breaks down. In addition, she will look for new invariants of symplectic 4-manifolds, and enlarge her own knowledge by studying the new methods recently introduced into symplectic topology, such as generating functions. Interactive activities at the host institution include: leading a seminar on New Developments in Symplectic Topology, and participating in the activities of the Noetherian Ring, the women graduate student group in the Mathematics department at Berkeley. This project furthers VPW program objectives which are (1) to provide opportunities for women to advance their careers in engineering and in the disciplines of science supported by NSF and (2) to encourage women to pursue careers in science and engineering by providing greater visibility for women scientists and engineers employed in industry, government, and academic institutions. By encouraging the participation of women in science, it is a valuable investment in the Nation's future scientific vitality.