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On Gromov Width under Deformations
Spencer Cattalani
We construct a uniformly bounded symplectic structure on admitting embeddings by arbitrarily large balls. This provides a counterexample to a recent conje…
Ahlfors Currents and Symplectic Non-Hyperbolicity
Spencer Cattalani
Complex (affine) lines are a major object of study in complex geometry, but their symplectic aspects are not well understood. Inspired by Duval's work on Ahlfors currents, we use t…
Positivity of Intersections and Tameness of Almost Complex 4-manifolds
Spencer Cattalani
We prove that pseudoholomorphic curves intersect complex 2-cycles positively in almost complex 4-manifolds. This makes possible a general and conceptually simple proof that an almo…
Coarsely Holomorphic Curves and Symplectic Topology
Spencer Cattalani
A taming symplectic structure provides an upper bound on the area of an approximately pseudoholomorphic curve in terms of its homology class. We prove that, conversely, an almost c…