Symplectic Topology (Mathematics)

McDuff博士将继续研究 辛四维流形 很长一段时间以来，她一直在使用 理论的J-全纯曲线，试图分类，和 已经非常成功地为一个有限的类， 流形（包含合适的2-球面的流形）。 述的方法 似乎已经到了极限。 与此同时，冈普夫和其他人 找到了一种新的方法来构造辛4-流形的例子。 麦克达夫博士提出了一个详细的分析的可能性， 这一结构，以确定确切的J-全纯 曲线方法失效。 此外，她还将寻找新的 辛4-流形的不变量，并扩大了自己的知识 通过研究最近引入辛的新方法， 拓扑，如生成函数。 主办机构的互动活动包括： 辛拓扑学新发展研讨会， 参加诺特环活动的妇女， 伯克利数学系的研究生小组。 本项目进一步促进了VPW计划的目标，即（1） 为妇女提供机会， 工程和科学的学科由NSF支持， (2)鼓励女性从事科学和工程职业 通过提高女性科学家和工程师的知名度， 受雇于工业、政府和学术机构。 通过 鼓励妇女参与科学，这是一个宝贵的 投资于国家未来的科学活力。

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.