16 citations · 79 across the 18 of their papers we have counts for
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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 expla…
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.…
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…
On Symplectic Packing Problems in Higher Dimensions
Kyler Siegel, Yuan Yao
Let denote the closed -dimensional symplectic ball of area , and let be a closed symplectic surface of genus and area . We prove that there is a…
Ellipsoidal superpotentials and singular curve counts
Dusa McDuff, Kyler Siegel
Given a closed symplectic manifold, we construct invariants which count (a) closed rational pseudoholomorphic curves with prescribed cusp singularities and (b) punctured rational p…
Ellipsoidal superpotentials and stationary descendants
Grigory Mikhalkin, Kyler Siegel
We compute stationary gravitational descendants in symplectic ellipsoids of any dimension, and use these to derive a number of new recursive formula for punctured curve counts in s…
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…
Higher Symplectic Capacities and the Stabilized Embedding Problem for Integral Ellipsoids
Dan Cristofaro-Gardiner, Richard Hind, Kyler Siegel
The third named author has been developing a theory of "higher" symplectic capacities. These capacities are invariant under taking products, and so are well-suited for studying the…
On the embedding complexity of Liouville manifolds
Sheel Ganatra, Kyler Siegel
We define a family of symplectic invariants which obstruct exact symplectic embeddings between Liouville manifolds, using the general formalism of linearized contact homology and i…
Computing higher symplectic capacities I
Kyler Siegel
We present recursive formulas which compute the recently defined "higher symplectic capacities" for all convex toric domains. In the special case of four-dimensional ellipsoids, we…
Counting curves with local tangency constraints
Dusa McDuff, Kyler Siegel
We construct invariants for any closed semipositive symplectic manifold which count rational curves satisfying tangency constraints to a local divisor. More generally, we introduce…
Higher symplectic capacities
Kyler Siegel
We construct new families of symplectic capacities indexed by certain symmetric polynomials, defined using rational symplectic field theory. In particular, we introduce a sequence…
Squared Dehn twists and deformed symplectic invariants
Kyler Siegel
We establish an infinitesimal version of fragility for squared Dehn twists around even dimensional Lagrangian spheres. The precise formulation involves twisting the Fukaya category…
Subflexible symplectic manifolds
Emmy Murphy, Kyler Siegel
We introduce a class of Weinstein domains which are sublevel sets of flexible Weinstein manifolds but are not themselves flexible. These manifolds exhibit rather subtle behavior wi…