Galois Theory and Elliptic Curves -- Bhargav Bhatt, June 14, 2004

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In this talk, we will try to describe the interactions between 
Galois Theory and the arithmetic of elliptic curves at an 
elementary level.  In particular, we will describe how the Galois
group acts on the torsion subgroup of an elliptic curve to give 
rise to a (Galois) representation.  Once this is achieved, we 
will mention some applications to mathematics (Fermat's last 
theorem) and crytography (Schoof's algorithm).  This talk will
conclude with a brief discussion of the B-SD conjecture and recent
results.