Gonality and the strong uniform boundedness conjecture for periodic points

Series
Athens-Atlanta Number Theory Seminar
Time
Monday, October 30, 2017 - 4:05pm for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Bjorn Poonen – Massachusetts Institute of Technology – https://math.mit.edu/~poonen/
Organizer
Joseph Rabinoff
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.