Thurston eigenvalues for unbounded postcritically finite rational maps

Holly Krieger (Cambridge)

Monday 20th March, 2017 16:00-17:00 Maths 204


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.

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