We conjecture that the relative Gromov–Witten potentials of elliptic fibrations are (cycle-
valued) lattice quasi-Jacobi forms and satisfy a holomorphic anomaly equation. We prove …

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 …

The virtual geometry of the moduli space of stable quotients is used to obtain Chow relations
among the kappa classes on the moduli space of nonsingular genus g curves. In a series of …

Let Mg, m be the moduli stack of prestable curves of genus g with m markings over the base
field k and let π: Cg, m→ Mg, m be the universal curve. Over Mg, m there exists the universal …

We construct and study various properties of a negative spin version of the Witten $ r $-spin
class. By taking the top Chern class of a certain vector bundle on the moduli space of twisted …

We establish new universal equations for higher genus Gromov–Witten invariants of target
manifolds, by studying both the Chern character and Chern classes of the Hodge bundle on …

THE GORENSTEIN PROPERTY AND PIXTON’S CONJECTURE FOR COMPACT TYPE
MODULI 1. Introduction 1.1. The tautological ring. Let M g,n Page 1 THE GORENSTEIN …

We define F-topological recursion (F-TR) as a non-symmetric version of topological
recursion, which associates a vector potential to some initial data. We describe the …

In this paper we prove, in a purely combinatorial-algebraic way, a structural quasi-
polynomiality property for the Bousquet-Mélou–Schaeffer numbers. Conjecturally, this …

Representations of vertex operator algebras define sheaves of coinvariants and conformal
blocks on moduli of stable pointed curves. Assuming certain finiteness and semisimplicity …