# Affine submanifolds of the moduli space of abelian differentials

## Alex Wright (U. Chicago)

Moduli spaces (strata) of abelian differentials (holomorphic one forms) on Riemann surfaces have a natural affine structure, in that they each have an atlas of charts to C^n with transition functions in GL(n,Z). I will discuss submanifolds of these moduli spaces that are locally defined by linear equations with real coefficients. The two dimensional case corresponds to Teichmuller curves. The main goal will be to explain how algebraic geometry may provide insight into recent conjectures coming from Teichmuller dynamics.

Tuesday, September 17th, at 4:00pm in HBH 227

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