Reference numberEC/1994/23
TitleMcDuff, Dusa: certificate of election to the Royal Society
DescriptionCitation typed
CitationDistinguished for work on functional analysis, diffeomorphism groups and symplectic geometry. In her early work on von Neumann algebras McDuff answered one of the main perplexing questions: how many tyupe II factors are there? She has also had a fundamental idea on central sequences which has influenced all subsequent work on type II factors. Her work on the group of volume-preserving diffeomorphisms is deep and fundamental with applications to foliations and mechanics. She is best known for her more recent work in symplectic geometry where she has been responsible for the most interesting known examples of symplectic structures including many surprises such as a non-Kahler simply connected symplectic 10-dimensional manifold and symplectic structures on 8 manifulds not determeined by their homology classes. She has developed a fine analysis of singularities of holomorphic curves in almost complex 4-manifolds which led her to a complete classification of symplectic 4-manifolds having an embedded symplectic two-sphere. Together with major works of Gromov and Eliashberg her results show that symplectic geometry is an extraordinarily fertile branch of mathematics that we are only beginning to explore.
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