I will discuss joint work with George Boxer, Frank Calegari, and Vincent Pilloni in which we prove the modularity of a positive proportion of abelian surfaces over Q.
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/faltings70