In [22, 23], Y.-P. Lee introduced a notion of universal relation for formal Gromov-Witten potentials. Universal relations are connected to tautological relations in the cohomology ring of the moduliâ€¦ (More)

In this paper we study relations between intersection numbers on moduli spaces of curves and Hurwitz numbers. First, we prove two formulas expressing Hurwitz numbers of (generalized) polynomials viaâ€¦ (More)

In [3] I. P. Goulden, D. M. Jackson, and R. Vakil formulated a conjecture relating certain Hurwitz numbers (enumerating ramified coverings of the sphere) to the intersection theory on a conjecturalâ€¦ (More)

In this paper, we collect a number of facts about double Hurwitz numbers, where the simple branch points are replaced by their more general analogues â€” completed (r + 1)-cycles. In particular, weâ€¦ (More)

We introduce the notion of Zwiebach invariants that generalize Gromov-Witten invariants and homotopical algebra structures. We outline the induction procedure that induces the structure of Zwiebachâ€¦ (More)

We propose a Hodge field theory construction that captures algebraic properties of the reduction of Zwiebach invari-ants to Gromov-Witten invariants. It generalizes the Barannikov-Kontsevichâ€¦ (More)

We derive the spectral curves for q-part double Hurwitz numbers, r-spin simple Hurwitz numbers, and arbitrary combinations of these cases, from the analysis of the unstable (0, 1)geometry. Weâ€¦ (More)

We introduce and study wheeled PROPs, an extension of the theory of PROPs which can treat traces and, in particular, solutions to the master equations which involve divergence operators. We constructâ€¦ (More)

DR-cycles are certain cycles on the moduli space of curves. Intuitively, they parametrize curves that allow a map to P1 with some specified ramification profile over two points. They are known to beâ€¦ (More)