Tropical geometry offers a combinatorial shadow of classical algebraic geometry. In this talk, we will explore tropical curves, which can be viewed as metric graphs with additional data, and their striking connections to the moduli space of algebraic curves. After introducing the basics of tropical curves, we will discuss how they form a moduli space that mirrors the classical compactification of M_{g,n}. We will also highlight the role of tropicalization in understanding degenerations and compactification.
Note that there is a lunch break at about noon, and after the break we will hold more informal discussions.