Cut and Paste Geometry -
A classical result in geometry is that any simple polygon can be cut into finitely many pieces are reassembled into a square with the same area.  Hilbert’s third problem asked whether or not we could also cut up a 3D polyhedron and reassemble it into a cube of the same volume, and Dehn showed that this is sometimes impossible.  In this talk, I will discuss the history of these problems, as well as generalizations to cut and paste problems on other geometric objects, like surface and manifolds.