Samir Canning: The Gorenstein question and Pixton's conjecture

Abstract

I will explain how to prove Pixton's conjecture on the structure of the tautological ring for some moduli spaces of curves of compact type of small genus, thereby completely determining the tautological ring in these cases. These examples are the first known cases where Pixton's conjecture holds but the tautological ring is not Gorenstein. As an application, I will explain that the tautological ring of the moduli space of genus g curves of compact type with n marked points is almost never Gorenstein, extending work of Petersen—Tommasi and Petersen in genus 2. This is joint work with Hannah Larson and Johannes Schmitt.