Lagrangian submanifolds are ubiquitous in symplectic geometry, and Lagrangian intersection or isotopy results underlie much of symplectic rigidity. On the other hand, given enough space, intersections can be eliminated and Lagrangians unknotted. Quantitative symplectic topology aims to determine how much space is required.
We will describe results on which Lagrangians can be moved into a fixed region under a Hamiltonian isotopy, and whether corresponding embeddings are knotted. Finally we discuss the size of Lagrangian complements, which have full measure but may not admit symplectic embeddings of large balls. Most of this is joint works with Ely Kerman, Emmanuel Opshtein and Jun Zhang.
