Symplectic embeddings and continued fractions: a survey
Symplectic Geometry
2009-10-14 v2 Number Theory
Abstract
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.
Keywords
Cite
@article{arxiv.0908.4387,
title = {Symplectic embeddings and continued fractions: a survey},
author = {Dusa McDuff},
journal= {arXiv preprint arXiv:0908.4387},
year = {2009}
}
Comments
Notes for the Takagi lectures, Sapporo, Japan, June 2009; 7 figures, v2: minor updates and changes