How does one measure distance between triangulations? What does the graph of the space of configurations of a Rubik’s cube look like? These questions might not seem directly related but both are questions about the geometry of combinatorial moduli spaces. Starting from examples of spaces coming from puzzles, the talk will be about the geometry of different configuration spaces.

Parts of the talk, and the image on the poster, are from a project called Mathema completed together with Paul Turner. The results on diameters of spaces of triangulations are joint with Valentina Disarlo and with Lionel Pournin.