8 papers
Lectures on stabilized ellipsoid embeddings
Kyler Siegel
These notes are based on a five-part minicourse on stabilized symplectic embeddings given in Les Marécottes, Switzerland during a September 2025 workshop. Our main goal is to expl…
Sesquicuspidal curves, scattering diagrams, and symplectic nonsqueezing
Dusa McDuff, Kyler Siegel
We solve the stabilized symplectic embedding problem for four-dimensional ellipsoids into the four-dimensional round ball. The answer is neatly encoded by a piecewise smooth functi…
Singular algebraic curves and infinite symplectic staircases
Dusa McDuff, Kyler Siegel
We show that the infinite staircases which arise in the ellipsoid embedding functions of rigid del Pezzo surfaces (with their monotone symplectic forms) can be entirely explained i…
Symplectic field theory: an overview
Richard Hind, Kyler Siegel
We summarize some of the main ideas and results around symplectic field theory, from its early inception up to recent and ongoing developments.
A tree formula for the ellipsoidal superpotential of the complex projective plane
Kyler Siegel
The ellipsoidal superpotential of the complex projective plane can be interpreted as a count of rigid rational plane curves of a given degree with one prescribed cusp singularity.…
Symplectic capacities, unperturbed curves, and convex toric domains
Dusa McDuff, Kyler Siegel
We use explicit pseudoholomorphic curve techniques (without virtual perturbations) to define a sequence of symplectic capacities analogous to those defined recently by the second n…