ECH capacities and applications to symplectic embeddings

I will talk about embedded contact homology capacities and some recent applications of it to obstructing symplectic embeddings. I will show how to compute ECH capacities of so-called concave toric domains and I will give some examples of when they give sharp obstructions to symplectic ball packings. In particular, I will discuss the case of the union of a ball with an infinite cylinder. This is joint work with K. Choi, D. Cristofaro-Gardiner, D. Frenkel and M. Hutchings.