He talked about the basic principles of origami design from the perspective of crease patterns. He identified four rules:
1) Two-colorability. The open spaces in a pattern can be colored in using two colors and no two adjacent spaces will be the same color.
2) M-V=+/-2 At any given vertex the number of mountain folds will be exactly two more or two less than the number of valley folds.
3) Around each vertex, alternate angles will sum to a straight line.
4) No self intersections of the paper.
For more, watch one of the videos provided by TED or the IMA (for the IMA find the Videos section and click on IMA Math Matters Public Lectures).
He also talked on the modern uses of origami technique and its applications in space, cars, medicine and science. He also answered questions and signed autographs.
I asked him if he thought there was a philosophy of origami. He said that if I asked a hundred folders that question I'd get as many different answers. That every folder has their own philosophy. Lang seems to be a technician at heart. He works out the techniques and the mechanisms so that others can do the art.