The tautological relation of moduli space of curves is a classical and important topic in algebraic geometry. Recently, Pandharipande, Pixton and Zvonkine proved a very general class of tautological relations by studying the shifted Witten class near the discriminant. Pixton further conjectured that these are all the relations.

In this talk I will introduce a new approach to obtaining tautological relations on $\overline{M}_{g,n}$ by using the (quasi)modularity of the shifted FJRW CohFT of $x^3+y^3+z^3$. Whether these tautological relations are different from Pixton’s relations is unknown. This is based on my work in progress.