Fox and Hedgehog Seminar - 'Optimization in paper geometry'

I have always tried to pick research problems that are simply stated and have an experimental feel to them, subject to the constraint that I have some possibility of solving them. In short, I do what I can. I will talk about my recent forays into optimization problems related to paper geometry. First, I’ll sketch my proof of the optimal paper Moebius band conjecture, which tells you how long a strip of paper you need in order to make a paper Moebius band. Second, I’ll sketch my proof of the minimal vertex problem for origami tori, which answers the question of how many vertices (or folds) you need to make a torus out of paper. The second topic has lots of computer demos.