Thurston eigenvalues for unbounded postcritically finite rational maps

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• Holly Krieger, Cambridge
• Wednesday 23 November 2016, 16:00-17:00
• MR13.

If you have a question about this talk, please contact Ivan Smith.

A postcritically finite (PCF) ramified covering map of the Riemann sphere induces a Thurston pullback map on the Teichmüller space of a Riemann surface of genus 0 with the post-critical set removed. Thurston’s topological characterization guarantees that the Thurston pullback of a rational PCF map will have a (unique) fixed point. The connection between the complex dynamics of a PCF rational function and the behavior of its induced pullback map at the fixed point is not yet well understood. I’ll discuss some possible connections, particularly for quadratic PCF maps, including a question of Buff-Epstein-Koch connecting boundedness in moduli space with the existence of a spectral gap for the pullback maps.

This talk is part of the Differential Geometry and Topology Seminar series.

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