On symplectic capacities of toric domains

Symplectic Capacities of Domains in C

Toric symplectic ball packing

We define and solve the toric version of the symplectic ball packing problem, in the sense of listing all 2n-dimensional symplectic–toric manifolds which admit a perfect packing by balls embedded in a symplectic and torus equivariant fashion. In order to do this we first describe a problem in geometric–combinatorics which is equivalent to the toric symplectic ball packing problem. Then we solve...

Symplectic Toric Manifolds

Foreword These notes cover a short course on symplectic toric manifolds, delivered in six lectures at the summer school on Symplectic Geometry of Integrable Hamiltonian Systems, mostly for graduate students, held at the Centre de Recerca Matemàtica in Barcelona in July of 2001. The goal of this course is to provide a fast elementary introduction to toric manifolds (i.e., smooth toric varieties)...

Symplectic Toric Varieties

These are the notes of two lectures given at the Mini Spring School An introduction to the mathematics of string theory held at Adelaide University in November 2002. It is a leisurely introduction to the mathematics surrounding toric varieties. Lecture I. Aims of Lecture I. (i) To contrast topological, Riemannian, symplectic and complex structures; (ii) to set up various topological objects tha...

Symplectic Topology and Capacities

I am going to talk about symplectic topology, a field that has seen a remarkable development in the past 15 years. Let’s begin with what was classically known – which was rather little. We start with a symplectic form ω, that is, a closed 2-form which is nondegenerate. This last condition means that ω is defined on an even dimensional manifold M and that its wedge with itself n times is a top d...