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SUMMARY:Reduction of dynatomic curves - Holly Krieger (University of Cambr
 idge)
DTSTART:20170606T133000Z
DTEND:20170606T143000Z
UID:TALK72481@talks.cam.ac.uk
CONTACT:G. Rosso
DESCRIPTION:Dynatomic curves parametrize n-periodic orbits of a one-parame
 ter family of polynomial dynamical systems. These curves lack the structur
 e of their arithmetic-geometric analogues (modular curves of level n) but 
 can be studied dynamically.  Morton and Silverman conjectured a dynamical 
 analogue of the uniform boundedness conjecture (theorems of Mazur\, Merel)
 \, asserting uniform bounds for the number of rational periodic points for
  such a family.  I will discuss recent work towards the function field ver
 sion of their conjecture\, including results on the reduction mod p of dyn
 atomic curves for the quadratic polynomial family z^2+c.
LOCATION:MR13
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