I survey the recent advances in the study of tautological classes on the moduli spaces of
curves. After discussing the Faber-Zagier relations on the moduli spaces of nonsingular …

Relations among tautological classes on the moduli space of stable curves are obtained via
the study of Witten's r-spin theory for higher r. In order to calculate the quantum product, a …

We prove a conjecture of Pixton, namely that his proposed formula for the double
ramification cycle on M ̄ g, n vanishes in codimension beyond g. This yields a collection of …

In this paper we describe some of the constructions of FJRW theory. We also briefly describe
its relation to Saito-Givental theory via Landau-Ginzburg mirror symmetry and its relation to …

The relations in the tautological ring of the moduli space M_g of nonsingular curves
conjectured by Faber-Zagier in 2000 and extended to the moduli space of stable pointed …

We give a criterion for extending a generically semisimple (not necessarily conformal)
Frobenius manifold locally near a smooth point of the discriminant to a cohomological field …

We use relations in the tautological ring of the moduli spaces $\overline {\mathcal {M}} _ {g,
n} $ derived by Pandharipande, Pixton, and Zvonkine from the Givental formula for the $ r …

We propose an algorithm to derive tautological relations from Pixton relations. We carry out
this algorithm explicitly to derive some results in genus 0, 1, 2, 3 and analyze the possibility …

Using the equivariant virtual cycle of the moduli space of stable maps to $[\mathbb
{C}/\mathbb {Z} _r] $, or equivalently, the vanishing of high-degree Chern classes of a …

The tautological ring of the moduli space of curves is the ring generated by algebraic cycles
of geometric origin. While it has been well-studied, its structure is not yet completely …