Symplectic Topology (Mathematics)

McDuff博士将继续她对辛4流形结构的研究。长期以来，她一直在尝试用j全纯曲线理论对它们进行分类，并在一类受限的流形（包含合适的2球的流形）上取得了相当大的成功。这种方法似乎已经到了极限。同时，Gompf等人发现了一种构造辛4流形实例的新方法。McDuff博士建议对这种构造的可能性进行详细分析，以确定j全纯曲线方法究竟在哪里失效。此外，她将寻找辛4流形的新不变量，并通过研究辛拓扑中最近引入的新方法，如生成函数，来扩大自己的知识面。在主办机构的互动活动包括：主持一个关于辛拓扑新发展的研讨会，并参加伯克利数学系的女研究生小组Noetherian Ring的活动。该项目进一步推进了VPW计划的目标，即(1)为女性提供在工程和NSF支持的科学学科中发展职业的机会；(2)通过为在工业、政府和学术机构工作的女性科学家和工程师提供更大的知名度，鼓励女性在科学和工程领域追求职业。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.