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Riemann surfaces, complex projective structures, and Bers' simultaneous uniformization

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OGGW02 - Actions on graphs and metric spaces

For a closed orientable surface $S$ of genus at least two, a quasi-Fuchsian representation $\pi_1(S) \to {\rm PSL }(2, {\rm C})$ is a convex cocomact representation, or equivalently a quasi-isometric embedding. By Bers’ simultaneous uniformization theorem, quasi-Fuchsian representations correspond bijectively to pairs of Riemann surface structures on $S$.   Each quasi-Fuchsian representation, more precisely, gives a pair of complex projective structures on its corresponding Riemann surfaces, such that those projective structures share the quasi-Fuchsian holonomy. In this talk, we discuss more general correspondence between pairs of isomonodromic complex projective structures and pairs of Riemann surface structures.

This talk is part of the Isaac Newton Institute Seminar Series series.

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