Joint work with Benjamin Matschke. We shall discuss practical
algorithms which solve Mordell equations by combining the method of
Faltings (Arakelov, Parsin, Szpiro) with the Shimura-Taniyama conjecture.
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3444
[3] http://www.mpim-bonn.mpg.de/node/246