Undergraduate Math Club Seminar
Across mathematics, one seeks to understand collections of all possible objects of a certain kind. In many contexts this is called a moduli space. In this talk, we will examine an important basic example of a moduli space: the collection of flat metrics on the 2-torus. Along the way, we will encounter the compactness results of Mahler and Mumford. While they generalize to seemingly very different results, for this moduli space they end up being equivalent.