I will address two problems about recognizing surface groups. The first one is the classical problem of classifying Poincaré duality groups in dimension 2. I will present a new approach to this, joint with Peter Kropholler. The second problem is about recognizing surface groups among one-relator groups. Here I will present a new partial result, joint with Giles Gardam and Alan Logan.
This video was produced by Newcastle University, Australia, as part of the Symmetries in Newcastle seminar series.
