The set of k-planes in a vector space V (the Grassmannian Gr(k, V)) has a natural geometric structure, giving an example of a moduli space. Similarly (modulo technical caveats) we can talk about a moduli space of algebraic curves of genus g, which has a useful compactification consisting of "stable" curves. In this talk I will give a gentle introduction to the moduli space of stable curves and provide some motivation for working with it, such as applications to counting curves on varieties.

Speaker(s): Michael Mueller (UM)