General Events - Department of Mathematics

Title: Intersection results for Lagrangian tori returning to the symplectic cylinder

Abstract

Let L(r, s) be a standard Lagrangian product torus in the 4-dimensional symplectic cylinder of capacity 1.  If r is at least 1/2 and  s is at least 1, then for any Hamiltonian diffeomorphsm of R^4 that maps L(r,s) back into the cylinder, the image of  L(r,s) must intersect one of the   Lagrangian tori of the form L(r,t) for t \geq s. I will discuss the proof of this result as well as some applications concerning the shape invariant of Hind and Zhang. This is joint work with Richard Hind.