**Date & Time:** Thursday, August 14, 2014, 16:00-17:00.

**Venue:** Ramanujan Hall

**Title:** Open image theorem of Serre

**Speaker:** Mohammed Zuhair, UCLA

**Abstract:** Let E be an elliptic curve, over a number field K, without complex multiplication. A theorem of Serre says that the image of the Galois representation of the absolute Galois group of K on the l-adic Tate module T_l(E) has open image in GL_2(Z_l).
We shall give an outline of Serre's original proof of this theorem, emphasizing the ideas involved.