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SUMMARY:Post-critically finite maps - Thomas Gauthier\, Université Paris-
 Saclay
DTSTART:20251022T131500Z
DTEND:20251022T141500Z
UID:TALK238567@talks.cam.ac.uk
CONTACT:Dhruv Ranganathan
DESCRIPTION:Post-critically finite (PCF) rational maps are rational maps o
 f the Riemann sphere with all their critical points with finite orbit unde
 r iteration. In the space of rational maps of the projective line with a g
 iven degree\, post-critically finite maps play a central role. They can be
  thought as the equivalent of CM elliptic curves in the modular curve\; in
  particular\, they are Zariski dense.\n\nIn this talk\, I will first intro
 duce certain arithmetic and dynamical motivations to the study of PCF maps
  and discuss some of their properties. I will also discuss their non-Zaris
 ki density among endomorphisms of the projective space of dimension k>1. T
 his is a result we proved recently in a joint work with Johan Taflin and G
 abriel Vigny.\n\n
LOCATION:MR13
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