The second day also had some very nice talks. Probably the talk I was looking most forward to was the talk of Stefan Felsner about "Exploiting Air Pressure to Map Floorplans on Point Sets". A floorplan is a dissection of a rectangle into smaller rectangles. All rectangles are axis aligned. The floorplan is realized on a point set, if every segment contains exactly one point of the point set. Stefan showed that for every floorplan, you can find a realization of an equivalent floorplan on every point set in general position. This is not only a nice result, Stefan used also some cool tools to prove it.
Another talk I liked was given by Nieke Aerts about "Straight Line Triangle Representation" (joint work with Stefan Felsner). Nieke talked about the following problem: Can I draw a planar graph, such that every face has the form of a triangle? To realize such drawings many vertices have to be adjacent to an angle of exactly 180°. The talk was about necessary and sufficient conditions that such drawings exist. There are still many open questions left. This problem seems related to the stretchability of combinatorial pseudo-triangulations, but the straight line triangle representations are more difficult to understand - at least for now.
The second invited talk was given by James McLurkin. James talked about geometric challenges in multi-robot systems and showed many nice videos.