Student Arithmetic Date:  Wednesday, February 06, 2013 Location:  3866 East Hall (3:00 PM to 4:00 PM) Title:  Local fields and Galois representations Abstract:   The goal of this talk is to present some of the tools from Galois theory and class field theory used to study the absolute Galois group of Q and its representations, a key component of the Shimura-Taniyama conjecture. We'll mainly be comparing the structure of the absolute Galois group of the rationals to the Galois groups of local (or even finite) fields, which are much simpler to describe. We'll also give a complete description (from class field theory) of one-dimensional representations of these groups using the so-called cyclotomic character. Time permitting, we'll briefly touch on general Galois representations, especially two-dimensional l-adic reps, since these are the specific representations used in the modularity conjecture. Speaker:  Jake Levinson Institution:  UM Event Organizer:        Edit this event (login required). Add new event (login required). For access requests and instructions, contact math-webmaster@umich.edu Back to previous page Back to UM Math seminars/events page.