Collaborative Number Theory Seminar at the CUNY Graduate Center
Co-organizers: Gautam Chinta, Brooke Feigon, Krzysztof Klosin,
Fall 2014 Schedule:
September 19: Lloyd
Title: Moduli spaces of arithmetic dynamical systems: invariants and fields of definition
Abstract: I shall describe how to use the classical invariant theory of binary forms to construct the moduli space, $M_d$, of degree $d$ arithmetic dynamical systems on the projective line (i.e. degree $d$ rational maps). In particular, I shall give an explicit description in the case $d=3$. I shall then discuss the issue of field of moduli verses field of definition, and show how to solve this problem explicitly for the spaces $M_d$.
October 10: Alexei Entin (IAS)
Title: On the Bateman-Horn conjecture for polynomials over large finite fields
Title: Gamma factors of GL_n(R)-distinguished representations of GL_n(C)
Abstract: An irreducible representation (\pi,V)
of GL_n(C) is called GL_n(R)-distinguished if
there exists a non-zero
continuous GL_n(R)-invariant functional L:V \to
C. In the talk we give a necessary condition
for GL_n(R)-distinction. As a corollary, we
prove that the Rankin-Selberg gamma factors of
\pi \times \pi' at s=1/2 for \pi,\pi' distinguished
representations of GL_m(C), GL_n(C)
respectively equals 1.
November 14: Thomas Tucker (University of Rochester)
November 21: Jonah Leshin (CUNY)
December 12: Xiaoqing Li (SUNY Buffalo)
Title: A standard zero free region for Rankin-Selberg L-functions on GL(n)
In this talk, we will derive a standard zero
free region for Rankin-Selberg L-function
L(s, fxf) where f is a tempered Maass form on GL(n).
The method is based on the theory of Eisenstein
series generalizing a work of Sarnak. This is a
joint work with D. Goldfeld.