I just heard that Jeremy Kahn has announced joint work with Vladimir Markovic showing that every hyperbolic 3-manifold contains an immersed, -injective surface. This is equivalent to showing that the fundamental group of every hyperbolic 3-manifold contains a subgroup isomorphic to the fundamental group of a surface. The abstract for Jeremy’s talk is on the conference web page. This is a long standing open problem that Henry Wilton wrote about on this blog back in February. I’m not at the conference, so I didn’t see the talk, but if any of you readers were ther and have anything to add, feel free to write in in the comments.