2009/08/30 by Dusa McDuff, McDuff, Dusa
Mathematics · #11J70 #32S25 #53D05 #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals #Number Theory (math.NT) #Symplectic Geometry (math.SG) #math.NT #math.SG #msc:11J70 #msc:32S25 #msc:53D05
paper · pdf · doi:10.48550/arxiv.0908.4387
Notes for the Takagi lectures, Sapporo, Japan, June 2009; 7 figures, v2: minor updates and changes
openalex publication_date 2009/08/30 · arxiv created 2009/10/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.