Embedding questions in symplectic geometry

As has been known since the time of Gromov's Nonsqueezing Theorem, symplectic embedding questions lie at the heart of symplectic geometry.

In the past few years we have gained significant new insight into the question of when there is a symplectic embedding of one basic geometric shape (such as a ball or ellipsoid)into another (such as an ellipsoid or torus). After a brief introduction to symplectic geometry, this talk will describe some of this progress, with particular emphasis on results in dimension four.