Collaborative Number Theory Seminar at the CUNY Graduate CenterCoorganizers: Gautam Chinta, Brooke Feigon, Krzysztof Klosin,
Maria Sabitova,
Lucien Szpiro. Fall 2014 Schedule:
September 19: Lloyd
West (CUNY) 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 BatemanHorn 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 nonzero
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 RankinSelberg 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 RankinSelberg Lfunctions on GL(n) Abstract:
In this talk, we will derive a standard zero
free region for RankinSelberg Lfunction
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.
