title: Recent progress on symplectic embedding problems in four dimensions.
abstract: We survey some recent progress on understanding when one four-dimensional symplectic manifold can be symplectically embedded into another. In 2010, McDuff established a number-theoretic criterion for the existence of a symplectic embedding of one four-dimensional ellipsoid into another. This result is related to previously known criteria for when a disjoint union of balls can be symplectically embedded into a ball. Numerical invariants defined using embedded contact homology give general obstructions to symplectic embeddings in four dimensions which turn out to be sharp in the above cases.
authors.affiliation: Department of Mathematics, University of California, Berkeley, California 94720, USA. hutching@math.berkeley.edu
authors.forename: Michael
authors.initials: M
authors.lastname: Hutchings