Séminaire de géométrie symplectique et de contact (archives)

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.

Building on Seidel-Solomon’s fundamental work, we define the notion of a g-equivariant Lagrangian brane in a symplectic manifold M if g ⊂ SH 1 (M ) is a sub-Lie algebra of symplectic cohomology of M . This allows us to construct a mirror theory to Bott-Borel-Weil theory on the A-side. We will make our construction completely explicit in the case of sl2 and comment on generalizations to arbitrary semisimple Lie algebras. This is a joint work with James Pascaleff.