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25 Dec 2009
Symplectic embeddings and continued fractions: a survey
 Dusa McDuff
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As has been known since the time of Gromov’s Nonsqueezing Theorem, symplectic embedding questions lie at the heart of symplectic geometry. After surveying some of the most important ways of measuring the size of a symplectic set, these notes discuss some recent developments concerning the question of when a 4dimensional ellipsoid can be symplectically embedded in a ball. This problem turns out to have unexpected relations to the properties of continued fractions and of exceptional curves in blow ups of the complex projective plane. It is also related to questions of lattice packing of planar triangles.
This article is based on the 6th Takagi Lectures that the author delivered at the Hokkaido University on June 6 and 7, 2009. A related course of lectures was also given at the MSRI Graduate Summer school in August 2009.
Dusa McDuff: partially supported by NSF grant DMS 0604769.
Communicated by: Kaoru Ono
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 Title
 Symplectic embeddings and continued fractions: a survey
 Journal

Japanese Journal of Mathematics
Volume 4, Issue 2 , pp 121139
 Cover Date
 20091201
 DOI
 10.1007/s1153700909269
 Print ISSN
 02892316
 Online ISSN
 18613624
 Publisher
 Springer Japan
 Additional Links
 Topics
 Keywords

 symplectic embedding
 symplectic capacity
 continued fractions
 symplectic ellipsoid
 symplectic packing
 lattice points in triangles
 53D05
 32S25
 11J70
 Authors

 Dusa McDuff ^{(1)}
 Author Affiliations

 1. Department of Mathematics, Barnard College, Columbia University, New York, NY, 100276598, USA