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Symplectic topology of some surface singularities

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  • UserEmily Maw (LSGNT)
  • ClockFriday 09 March 2018, 15:00-16:00
  • HouseMR13.

If you have a question about this talk, please contact Nils Prigge.

When you smooth a singularity in a symplectic manifold, you introduce some extra topology in its place: a Lagrangian vanishing cycle. Hence questions about degenerations of algebraic surfaces can be rephrased in terms of Lagrangian embeddings of 2D cell complexes. We will meet certain cell complexes called “pinwheels” (vanishing cycles of Wahl singularities), whose Lagrangian embeddings in CP2 are classified by so-called Markov numbers (by work of Evans-Smith). I will talk a bit about my work on extending this to other surfaces, and give an idea of the proof in the case of P1 x P1, which uses holomorphic curve techniques. The talk should be accessible to all, regardless of symplectic background (or lack thereof!).

This talk is part of the Junior Geometry Seminar series.

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