5-6pm in LGRT 1528.
Abstract: I will motivate and introduce several important concepts from differential geometry, particularly those pertaining to the shapes of surfaces. This means I will talk about different ways of measuring how “curved” a surface is and how one can go about recovering the complete shape of a surface if one knows its curvature. Finally, I will sketch an important theorem of Aleksandrov that says that the only “round surface” is the sphere, an interesting feature of this theorem is that the only known proofs rely on methods from analysis and partial differential equations.