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Dusa McDuff, Barnard College and Columbia University

Abstract: As has been known since the time of Gromov's Nonsqueezing Theorem, symplectic embedding uestions lie at the heart of symplectic geometry. In the past few years we have gained significant ew insight into the question of when there is a symplectic embedding of one basic geometric shape such as an ellipsoid or polydisc) into another, specially in dimension four. In many cases the nswers are quite surprising, relating to questions of symplectic dynamics and to elementary number theory.