Gonality and the strong uniform boundedness conjecture for periodic points

Series: 
Athens-Atlanta Number Theory Seminar
Monday, October 30, 2017 - 16:05
1 hour (actually 50 minutes)
Location: 
Skiles 005
,  
Massachusetts Institute of Technology
Organizer: 
The function field case of the strong uniform boundedness conjecturefor torsion points on elliptic curves reduces to showing thatclassical modular curves have gonality tending to infinity.We prove an analogue for periodic points of polynomials under iterationby studying the geometry of analogous curves called dynatomic curves.This is joint work with John R. Doyle.