I recently started reading Étienne Ghys slides on knots and dynamics <http://www.umpa.ens-lyon.fr/~ghys/articles/icm.pdf> which seem very interesting. I know this approach to knots and dynamics is not entirely new, for instance, this is from the 1980's <http://www.math.columbia.edu/~jb/bw-KPO-I.pdf>. This post gave me the impression that it is a promising topic http://terrytao.wordpress.com/2007/08/03/2006-icm-etienne-ghys-knots-and-dynamics/. Two questions: (the second one is pretty general and I don't expect to have a response if someone finds it not too appropriate for this site, although an answer is always tremendously appreciated)

1. Are there any recent breakthroughs after the release of these Ghys's slides that I should pay attention to?
2. Can anyone think of a research opportunity related to this topic for a not too long master's thesis project?

I find it a very interesting topic and convenient to combine the expertise in knots of my current adviser and my interest in dynamic and ergodic theory.