Related papers: Double ramification cycles and the $n$-point funct…

We identify the formulas of Buryak and Okounkov for the n-point functions of the intersection numbers of psi-classes on the moduli spaces of curves. This allows us to combine the earlier known results and this one into a principally new…

Using the celebrated Witten-Kontsevich theorem, we prove a recursive formula of the $n$-point functions for intersection numbers on moduli spaces of curves. It has been used to prove the Faber intersection number conjecture and motivated us…

DR-cycles are certain cycles on the moduli space of curves. Intuitively, they parametrize curves that allow a map to \mathbb{P}^1 with some specified ramification profile over two points. They are known to be tautological classes, but in…

We present a series of new results we obtained recently about the intersection numbers of tautological classes on moduli spaces of curves, including a simple formula of the n-point functions for Witten's $\tau$ classes, an effective…

We prove a new effective recursion formula for computing all intersection indices (integrals of $\psi$ classes) on the moduli space of curves, inducting only on the genus.

Using the connection between intersection theory on the Deligne-Mumford spaces and the edge scaling of the GUE matrix model (see math.CO/9903176, math.AG/0101147), we express the n-point functions for the intersection numbers as…

Inside the moduli space of curves of genus 2 with 2 marked points we consider the loci of curves admitting a map to P^1 of degree d totally ramified over the two marked points, for d>= 2. Such loci have codimension two. We compute the class…

Curves of genus g which admit a map to CP1 with specified ramification profile mu over 0 and nu over infinity define a double ramification cycle DR_g(mu,nu) on the moduli space of curves. The study of the restrictions of these cycles to the…

We compute the classes of universal theta divisors of degrees zero and g-1 over the Deligne-Mumford compactification of the moduli space of curves, with various integer weights on the points, in particular reproving a recent result of…

We study the intersection ring of the space $\M(\alpha_1,...,\alpha_m)$ of polygons in $\R^3$. We find homology cycles dual to generators of this ring and prove a recursion relation in $m$ (the number of steps) for their intersection…

Let X be a nonsingular projective algebraic variety, and let S be a line bundle on X. Let A = (a_1,..., a_n) be a vector of integers. Consider a map f from a pointed curve (C,x_1,...,x_n) to X satisfying the following condition: the line…

Kontsevich's work on Airy matrix integrals has led to explicit results for the intersection numbers of the moduli space of curves. In this article we show that a duality between k-point functions on $N\times N$ matrices and N-point…

We describe double Hurwitz numbers as intersection numbers on the moduli space of curves. Assuming polynomiality of the Double Ramification Cycle (which is known in genera 0 and 1), our formula explains the polynomiality in chambers of…

This survey grew out of notes accompanying a cycle of lectures at the workshop Modern Trends in Gromov-Witten Theory, in Hannover. The lectures are devoted to interactions between Hurwitz theory and Gromov-Witten theory, with a particular…

We describe algorithms for computing the intersection numbers of divisors and of Chern classes of the Hodge bundle on the moduli spaces of stable pointed curves. We also discuss the implementations and the results obtained. There are…

This article is an extended version of preprint math.AG/9902104. We find an explicit formula for the number of topologically different ramified coverings of a sphere by a genus g surface with only one complicated branching point in terms of…

In this paper we study effective recursion formulae for computing intersection numbers of mixed $\psi$ and $\kappa$ classes on moduli spaces of curves. By using the celebrated Witten-Kontsevich theorem, we generalize Mulase-Safnuk form of…

We prove a closed formula for the integral of a power of a single $\psi$-class on strata of $k$-differentials. In many cases, these integrals correspond to intersection numbers on twisted double ramification cycles. Then we conjecture an…

Goulden, Jackson and Vakil observed a polynomial structure underlying one-part double Hurwitz numbers, which enumerate branched covers of $\mathbb{CP}^1$ with prescribed ramification profile over $\infty$, a unique preimage over 0, and…

We introduce a new method of calculating intersections on \bar{M}_{g,n}, using localization of equivariant cohomology. As an application, we give a proof of Mirzakhani's recursion relation for calculating intersections of mixed psi and…