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Monday, October 30, 2017 - 17:15 ,
Location: Skiles 005 ,
Spencer Bloch ,
University of Chicago ,
Organizer: Joseph Rabinoff

Golyshev and Zagier found an interesting new source of periods associated to (eventually inhomogeneous) solutions generated by the Frobenius method for Picard Fuchs equations in the neighborhood of singular points with maximum unipotent monodromy. I will explain how this works, and how one can associate "motivic Gamma functions" and generalized Beilinson style variations of mixed Hodge structure to these solutions. This is joint work with M. Vlasenko.

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.