Stable tree expressions with Omega-classes and Double Ramification cycles

Abstract

We propose a new system of conjectural relations in the tautological ring of the moduli space of curves involving stable rooted trees with level structure decorated by Hodge and Ω-classes and prove these conjectures in different cases.

References in corpus (14)

• Towards an enumerative geometry of the moduli space of twisted curves and r-th roots
• Double ramification cycles and integrable hierarchies
• admcycles -- a Sage package for calculations in the tautological ring of the moduli space of stable curves
• Tau-structure for the Double Ramification Hierarchies
• Loop equations and a proof of Zvonkine's $qr$-ELSV formula
• DR/DZ equivalence conjecture and tautological relations
• Chiodo formulas for the r-th roots and topological recursion
• Double Hurwitz numbers: polynomiality, topological recursion and intersection theory
• Flat F-manifolds, F-CohFTs, and integrable hierarchies
• Masur-Veech volumes and intersection theory: the principal strata of quadratic differentials
• Higher genus relative Gromov--Witten theory and DR-cycles
• The quantum Witten-Kontsevich series and one-part double Hurwitz numbers
• An intersection-theoretic proof of the Harer-Zagier formula
• A conjectural formula for $D{R}_g(a,-a){\lambda }_g$