For the moduli space of stable curves Mg-bar, we can define its slope, call it s_g. In the talk, I will focus on two open questions:

Why do we care about the slope? One reason is that it can help us understand the pseudo-effective cone of Mg-bar. Another reason is that it has a strong geometric interpretation. For example, the Harris-Mumford theorem on the Kodaira dimension of Mg-bar is equivalent to the inequality s_g < 13/2, for g>23. If time permits, I will further talk about the moduli space of principally polarized abelian variety, Ag-bar, and how the answer to question (2) will determine whether or not Ag-bar is fundamentally different from Mg-bar.