Abstract:

The study of symplectic embeddings has a long history starting with the celebrated Gromov's non-squeezing theorem. One of the long-standing conundrums in the field was the ellipsoid embedding problem. The answer to it is now known under the name of the Hofer conjecture which was proved by Dusa McDuff in 2011. In the talk, I will introduce ECH-capacities invented by Hutchings and give an overview of McDuff's proof which is based on this promising tool.