Counting pseudo-holomorphic curves in symplectic six-manifolds

Abstract: The signed count of embedded pseudo-holomorphic curves in a symplectic manifold typically depends on the choice of an almost complex structure on the manifold and so does not lead to a symplectic invariant. However, I will discuss two instances in which such naive counting does define a symplectic invariant. The proof of invariance combines methods of symplectic geometry with results of geometric measure theory, especially regularity theory for calibrated currents. The talk is based on joint work with Thomas Walpuski. Time permitting, I will also discuss a related project, joint with Eleny Ionel and Thomas Walpuski, whose goal is to use geometric measure theory to prove the Gopakumar-Vafa finiteness conjecture.

algebraic geometrydifferential geometrygeometric topologysymplectic geometry

Audience: researchers in the topic

Free Mathematics Seminar

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