Beyond Symplectic Geometry (Beyond Symplectic Geometry)

Symplectic geometry was created as the mathematical foundation of classical mechanics. At the start of the
twentieth century it became the foundation also of quantum mechanics. And since the advent of string theory it
has played a key role in quantum field theory too. The aim of this project is to take the ideas and techniques of
symplectic geometry and apply them to new fields, not in physics, but in geometry itself. We will attack a wide
variety of problems, from studying surfaces which minimise area to spaces with negative curvature. These
areas are, at first sight, unrelated to symplectic geometry. By bringing symplectic techniques to bear on these
questions we will be able to make progress where none was previously possible. To do this, we will need to
refine the techniques themselves, which will also lead to progress in symplectic geometry itself.