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SUMMARY:Complex dynamics: degenerations\, and irreducibility problems - Ro
 hini Ramadas\, University of Warwick
DTSTART:20221012T131500Z
DTEND:20221012T141500Z
UID:TALK178931@talks.cam.ac.uk
CONTACT:Dhruv Ranganathan
DESCRIPTION:Per_n is an affine algebraic curve\, defined over Q\, parametr
 izing (up to change of coordinates) degree-2 self-morphisms of P^1 with an
  n-periodic ramification point. The n-th Gleason polynomial G_n is a polyn
 omial in one variable with Z-coefficients\, whose vanishing locus parametr
 izes (up to change of coordinates) degree-2 self-morphisms of C with an n-
 periodic ramification point. Two long-standing open questions in complex d
 ynamics are: (1) Is Per_n is irreducible over C? (2) Is G_n is irreducible
  over Q? \n\nWe show that if G_n is irreducible over Q\, then Per_n is irr
 educible over C. In order to do this\, we find a Q-rational smooth point o
 f a projective completion of Per_n. This Q-rational smooth point represent
 s a special degeneration of degree-2 morphisms\, and as such admits a trop
 ical interpretation.
LOCATION:CMS MR13
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