Tag Archives: geodesic flow

Roth’s theorem

I am in Kyoto right now, attending the twenty-first Nevanlinna colloquium (update: took a while to write this post – now I’m in Sydney for the Clay lectures). Yesterday, Junjiro Noguchi gave a plenary talk on Nevanlinna theory in higher dimensions … Continue reading

Posted in Diophantine approximation, Ergodic Theory | Tagged , , , | 10 Comments

Surface subgroups in hyperbolic 3-manifolds

I just learned from Jesse Johnson’s blog that Vlad Markovic and Jeremy Kahn have announced a proof of the surface subgroup conjecture, that every complete hyperbolic -manifold contains a closed -injective surface. Equivalently, contains a closed surface subgroup. Apparently, Jeremy … Continue reading

Posted in 3-manifolds, Ergodic Theory, Surfaces | Tagged , , , , , , , , | 10 Comments