The moduli space M_{g,n} of smooth algebraic curves of genus g with n distinct marked points is not compact. However, it admits many compactifications that are themselves moduli spaces, and it remains an outstanding problem in algebraic geometry to classify these modular compactifications. An important family of examples is that of the moduli spaces of “weighted pointed” curves constructed by Hassett, in which a vector of real numbers determines which of the n marked points are permitted to come together. In this talk, I will present joint work with Vance Blankers that constructs modular compactifications of M_{g,n} using a simplicial complex rather than vector of weights as an input. Not only do the resulting “simplicial” moduli spaces generalize Hassett’s, but they also classify the modular compactifications coming from colliding markings. If time permits, we will also discuss how this idea can be combined with an earlier classification result to produce a classification of modular compactifications of M_{1,n} by Gorenstein curves admitting collisions.

Location: ENR2 S395