I will give a survey of some of the most important results in 3-manifold topology since Perelman's proof of the Geometrization Conjecture. Due to the recent results of Agol, Calegari-Gabai, Kahn-Markovic and Wise we now have a much better understanding of 3-manifolds. Especially the new methods introduced by Wise hold the promise to be very useful in the near future. If time permits, then I will also talk about several applications to symplectic 4-manifolds and minimal complexity of surfaces in 4-manifolds.
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/3651