Monday, October 30, 2017 - 16:05 , Location: Skiles 005 , Bjorn Poonen , Massachusetts Institute of Technology , 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.
Thursday, April 14, 2016 - 17:15 , Location: Skiles 006 , Zhiwei Yun , Stanford University , Organizer: Matt Baker
In joint work with Wei Zhang, we prove a higher derivative analogue of the Waldspurger formula and the Gross-Zagier formula in the function field setting under the assumption that the relevant objects are everywhere unramified. Our formula relates the self-intersection number of certain cycles on the moduli of Shtukas for GL(2) to higher derivatives of automorphic L-functions for GL(2).
Thursday, April 14, 2016 - 16:05 , Location: Skiles 006 , Melanie Matchett-Wood , University of Wisconsin , Organizer: Matt Baker
The Cohen-Lenstra Heuristics conjecturally give the distribution of class groups of imaginary quadratic fields. Since, by class field theory, the class group is the Galois group of the maximal unramified abelian extension, we can consider the Galois group of the maximal unramified extension as a non-abelian generalization of the class group. We will explain non-abelian analogs of the Cohen-Lenstra heuristics due to Boston, Bush, and Hajir and joint work with Boston proving cases of the non-abelian conjectures in the function field analog.