As has been known since the time of Gromov's Nonsqueezing
Theorem, symplectic embedding questions lie at the heart
of symplectic geometry. These talks will 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 exceptional curves in blow ups of the
complex projective plane.