Enumerative geometry of ellipsoids
I will introduce enumerative invariants which count curves with local tangency constraints in a symplectic manifold. For closed manifolds, we give an algorithm which computes these invariants in terms of previously known blowup Gromov-Witten invariants. For open manifolds, these invariants can be used to define a new family of symplectic capacities. I will describe work in progress which recursively computes these invariants for all convex toric domains. As a consequence, we get many new obstructions for higher dimensions ellipsoid embeddings. This is partly based on joint work with Dusa McDuff.