辛嵌入与连分数
Symplectic embeddings and continued fractions: a survey
摘要：
自Gromov的非压缩定理以来，辛嵌入问题一直是辛几何的核心问题。在调查了一些最重要的测量辛集的大小的方法之后，这些笔记讨论了关于四维椭球何时可以辛嵌入球的问题的一些最新进展。这个问题与复射影平面的连分数和例外曲线的性质有意想不到的关系。它也涉及到平面三角形的格填充问题。
英文摘要：
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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