Abstract: In this talk, we will explore some properties of Chern classes. In the axiomatic way, these properties uniquely determine these Chern classes.

Abstract: Examples will be given to convince you that I do not know when a closed subset of a Riemann surface is a set of uniform approximation by holomorphic or meromorphic functions.

Abstract: A planar tiling is a repeating symmetric pattern in the plane. Because of their common everyday appearances such patterns are called "wallpaper groups." We follow Conway's orbifold notation, which describes the 17 wallpaper groups as certain topological spaces: quotients of the plane by some finite group. Completeness is given by computing the Euler characteristic of such spaces. No knowledge of groups, topology, orbifolds, or how to hang wallpaper required.