Chamber structure and Double Hurwitz numbers

Paul Johnson (Imperial College)

Monday 8th February, 2010 16:00-17:00 Mathematics Building, room 204


Hurwitz numbers count maps between complex curves with specified ramification. Goulden, Jackson and Vakil have proven that double Hurwitz numbers are piecewise polynomial, and conjectured a deep geometric explanation for a part of this fact. I will discuss joint work with R. Cavalieri and H. Markwig that reproves and refines the piecewise polynomiality result of GJV: in particular, we determine the regions of polynomiality and give wall crossing formulas. Our methods are elementary, and involve concrete manipulations of graphs and hyperplane arrangements. However, our work contains several suggestive shadows of the geometry conjectured by GJV, which I hope to mention.

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