Logarithmic geometry adds extra structure to geometric objects in a way that sometimes allows degenerate geometric objects (e.g., nodal curves) to behave as if they were non-degenerate (e.g., smooth). This can sometimes suggest ways to add a boundary to a non-compact moduli space. For example, the Deligne-Mumford compactification of the moduli space of curves can be recovered as the moduli space of smooth logarithmic curves.

I will try to offer intuition about logarithmic structures and the information they encode. We will discuss several examples expanding on the relationship between logarithmic curves and the Deligne-Mumford compactification. Speaker(s): Jonathan Wise (Colorado)