# Cut-and-join operators for higher Weil-Petersson volumes

@inproceedings{Alexandrov2021CutandjoinOF, title={Cut-and-join operators for higher Weil-Petersson volumes}, author={Alexander Alexandrov}, year={2021} }

In this paper, we construct the cut-and-join operator description for the generating functions of all intersection numbers of ψ, κ, and Θ classes on the moduli spaces Mg,n. The cut-and-join operators define an algebraic version of topological recursion. This recursion allows us to compute all these intersection numbers recursively. For the specific values of parameters, the generating functions describe the volumes of moduli spaces of (super) hyperbolic Riemann surfaces with geodesic boundaries…

## References

SHOWING 1-10 OF 20 REFERENCES

Weil-Petersson volumes and intersection theory on the moduli space of curves

- Mathematics
- 2006

In this paper, we establish a relationship between the Weil-Petersson volume Vgin(b) of the moduli space Mg,n(b) of hyperbolic Riemann surfaces with geodesic boundary components of lengths b\,...,bn,…

KP integrability of triple Hodge integrals. III. Cut-and-join description, KdV reduction, and topological recursions

- Mathematics, Physics
- 2021

In this paper, we continue our investigation of the triple Hodge integrals satisfying the Calabi–Yau condition. For the tau-functions, which generate these integrals, we derive the complete families…

Recursion Between Mumford Volumes of Moduli Spaces

- Mathematics, Physics
- 2007

We propose a new proof, as well as a generalization of Mirzakhani’s recursion for volumes of moduli spaces. We interpret those recursion relations in terms of expectation values in Kontsevich’s…

Recursion Formulae of Higher Weil–Petersson Volumes

- Mathematics
- 2008

In this paper, we study effective recursion formulae for computing intersection numbers of mixed and classes on moduli spaces of curves. By using the celebrated Witten-Kontsevich theorem, we…

CUT-AND-JOIN OPERATOR REPRESENTATION FOR KONTSEVICH–WITTEN TAU-FUNCTION

- Physics, Mathematics
- 2011

In this short note we construct a simple cut-and-join operator representation for Kontsevich–Witten tau-function that is the partition function of the two-dimensional topological gravity. Our…

Cut-and-join description of generalized Brezin-Gross-Witten model

- Physics, Mathematics
- 2016

We investigate the Brezin-Gross-Witten model, a tau-function of the KdV hierarchy, and its natural one-parameter deformation, the generalized Brezin-Gross-Witten tau-function. In particular, we…

Towards an Enumerative Geometry of the Moduli Space of Curves

- Mathematics
- 1983

The goal of this paper is to formulate and to begin an exploration of the enumerative geometry of the set of all curves of arbitrary genus g. By this we mean setting up a Chow ring for the moduli…

GROMOV-WITTEN INVARIANTS OF P1 COUPLED TO A KDV TAU FUNCTION

- 2018

We consider the pull-back of a natural sequence of cohomology classes Θg,n ∈ H2(2g−2+n)(Mg,n) to the moduli space of stable mapsM n(P, d). These classes are related to the Brézin-Gross-Witten tau…

Enumerative geometry via the moduli space of super Riemann surfaces

- Mathematics, Physics
- 2020

In this paper we relate volumes of moduli spaces of super Riemann surfaces to integrals over the moduli space of stable Riemann surfaces $\overline{\cal M}_{g,n}$. This allows us to use a recursion…

JT gravity as a matrix integral

- Physics
- 2019

We present exact results for partition functions of Jackiw-Teitelboim (JT) gravity on two-dimensional surfaces of arbitrary genus with an arbitrary number of boundaries. The boundaries are of the…