Abstract: This talk will focus on a geometric construction called compactified configuration spaces, where the resolution of point collisions can be seen as a real analogue of the Deligne–Mumford compactification of the moduli spaces of marked Riemann surfaces. I will talk about the local “bubbling” behavior, which globally has an iterative nature and is encoded in a combinatorial “tree” structure. This new construction has been an essential tool in the study of constant curvature conical metrics in the recent joint works with Rafe Mazzeo. We expect this construction to be useful in the study of the L^2 cohomology and intersection cohomology of moduli spaces of singular metrics.