Gonality and the strong uniform boundedness conjecture for periodic points

Athens-Atlanta Number Theory Seminar
Monday, October 30, 2017 - 4:05pm
1 hour (actually 50 minutes)
Skiles 005
Massachusetts Institute of Technology
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.