Planar graph colorings and pseudo-holomorphic curves

Planar graph colorings and pseudo-holomorphic curves

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Emmy Murphy, Northwestern University/IAS
Fine Hall 314

Associated to a planar, trivalent graph, we can define a surface in R^5. Here R^5 is naturally equipped with a geometry called a contact structure which the surface is compatible with. We discuss how many of the graph-theoretic properties and operations are related with their Legendrian counterparts, particularly the way that the chromatic polynomial of the graph is related to the symplectic field theory.