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Geometry, Symmetry and Physics Seminar

Enumerative geometry of ellipsoids

Kyler Siegel, Columbia

Location:  Hill Center 525
Date & time: Thursday, 12 December 2019 at 11:00AM - 12:00PM


Abstract: I will introduce enumerative invariants which count curves with local tangency constraints in a symplectic manifold. For closed manifolds, we give an algorithm which computes these invariants in terms of previously known blowup Gromov-Witten invariants. For open manifolds, these invariants can be used to define a new family of symplectic capacities. I will describe work in progress which recursively computes these invariants for all convex toric domains. As a consequence, we get many new obstructions for symplectic embeddings of ellipsoids in higher dimensions. This is partly based on joint work with Dusa McDuff.