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.
