"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.