"Diophantine equations via Galois representations"
Imin Chen, Simon Fraser University
Recently, the use of Galois representations attached to elliptic
curves has been used to resolve several cases of the generalized Fermat
equation. In this talk, I will discuss the method and some further cases which
can be analyzed at least partially, including the equation a^2+ b^2p = c^r,
where r = 3 or 5. Although a complete resolution is not yet possible, a
computational criterion can be obtained for r = 3, based on previous work by
Bennett-Skinner and Kraus. For r = 5, I outline a possible strategy using
a combination of quadratic Q-curves and elliptic curves over Q.