TITLE: Effective versions of Serre's theorem for elliptic curves 

ABSTRACT: A celebrated theorem of Serre from 1972 asserts that if E is an elliptic curve defined over the field of rational numbers, without Complex Multiplication, then its associated mod l representation is surjective for any sufficiently large prime l. In my talk I will discuss the question of what "sufficiently large" means in Serre's Theorem.