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Boundary stratifications of Hurwitz spaces

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If you have a question about this talk, please contact Kelly Wang .

A Hurwitz space is a moduli space parametrising holomorphic maps of Riemann surfaces with prescribed branching data. Building on work of Harris-Mumford, Abramovich-Corti-Vistoli describe a smooth compactification whose boundary parametrises degenerate maps. The boundary decomposes into connected subsets, or strata, corresponding to combinatorial types of degenerations. I will present recent results giving an explicit, implementable description of the strata. This description leads to a natural definition of a tropical Hurwitz space and has applications in complex dynamics.

This talk is part of the Junior Geometry Seminar series.

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