# Mathematics Colloquia and Seminars

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### Obstructions to symplectic embeddings in four dimensions

**Geometry/Topology**

Speaker: | Michael Hutchings, UC Berkeley |

Location: | 2112 MSB |

Start time: | Tue, May 28 2013, 3:10PM |

We discuss the question of when one symplectic four-manifold with boundary (such as star-shaped domain in R^4) can be symplectically embedded into another. Embedded contact homology can be used to define a sequence of obstructions, which are sharp in some cases (for example for embedding one ellipsoid into another, as shown by McDuff). For basic examples these obstructions can be computed combinatorially in terms of counting lattice points in polygons, but many open questions remain.