Symplectic embeddings and continued fractions: a survey

Details Symplectic embeddings and continued fractions: a survey Symplectic embeddings and continued fractions: a survey

2009-08-30

arxiv.org/abs/0908.4387v2

Mathematics

Symplectic Geometry

Notes for the Takagi lectures, Sapporo, Japan, June 2009; 7 figures, v2: minor updates and changes

Scientific paper

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 4-dimensional 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.

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