Related papers: Hodge-GUE correspondence and the discrete KdV equa…
A conjectural relationship between the GUE partition function with even couplings and certain special cubic Hodge integrals over the moduli spaces of stable algebraic curves is under consideration.
The Hodge-FVH correspondence establishes a relationship between the special cubic Hodge integrals and an integrable hierarchy, which is called the fractional Volterra hierarchy. In this paper we prove this correspondence. As an application…
We show that the generating series of some Hodge integrals involving one or two partitions are tau-functions of the KP hierarchy or the 2-Toda hierarchy respectively. We also formulate a conjecture on the connection between relative…
Okounkov [36] proved a remarkable formula relating $n$-point GUE (Gaussian unitary ensemble) correlators of a fixed genus to Witten's intersection numbers of the same genus. The partition function of GUE correlators is a tau-function for…
We establish an explicit relationship between the partition function of certain special cubic Hodge integrals and the generalized Brezin--Gross--Witten (BGW) partition function, which we refer to as the Hodge-BGW correspondence. As an…
We prove some combinatorial results related to a formula on Hodge integrals conjectured by Mari\~no and Vafa. These results play important roles in the proof and applications of this formula by the author jointly with Chiu-Chu Melissa Liu…
A conjecture on the relation between the cubic Hodge integrals and the topological vertex in topological string theory is resolved. A central role is played by the notion of generalized shift symmetries in a fermionic realization of the…
In this note we derive some consequences from the Mari\~no-Vafa formula and the cut-and-join equation, these include unified simple proofs of the $\lambda_g$ conjecture and some other Hodge integral identities. We also describe a proof of…
We prove a formula for certain cubic $\Z_n$-Hodge integrals in terms of loop Schur functions. We use this identity to prove the Gromov-Witten/Donaldson-Thomas correspondence for local $\Z_n$-gerbes over $\proj^1$.
We propose a conjectural formula expressing the generating series of some Hodge integrals in terms of representation theory of Kac-Moody algebras. Such generating series appear in calculations of Gromov-Witten invariants by localization…
We consider the Laguerre partition function, and derive explicit generating functions for connected correlators with arbitrary integer powers of traces in terms of products of Hahn polynomials. It was recently proven that correlators have a…
Based on the matrix-resolvent approach, for an arbitrary solution to the discrete KdV hierarchy, we define the tau-function of the solution, and compare it with another tau-function of the solution defined via reduction of the Toda lattice…
We prove the Gopakumar-Marino-Vafa formula for special cubic Hodge integrals. The GMV formula arises from Chern-Simons/string duality applied to the unknot in the three sphere. The GMV formula is a q-analog of the ELSV formula for linear…
Based on the duality between open-string theory on noncompact Calabi-Yau threefolds and Chern-Simons theory on three manifolds, M Marino and C Vafa conjectured a formula of one-partition Hodge integrals in term of invariants of the unknot…
We outline a proof of a remarkable formula for Hodge integrals conjectured by Marino and Vafa in hep-th/0108064 base on large N duality.
For an arbitrary semisimple Frobenius manifold we construct Hodge integrable hierarchy of Hamiltonian partial differential equations. In the particular case of quantum cohomology the tau-function of a solution to the hierarchy generates the…
Degenerate contributions to higher genus Gromov-Witten invariants of Calabi-Yau 3-folds are computed via Hodge integrals. The vanishing of contributions of covers of elliptic curves conjectured by Gopakumar and Vafa is proven. A formula for…
In this paper, we present an explicit formula that connects the Kontsevich-Witten tau-function and the Hodge tau-function by differential operators belonging to the $\hat{GL(\infty)}$ group. Indeed, we show that the two tau-functions can be…
We prove a remarkable formula for Hodge integrals conjectured by Marino and Vafa based on large N duality, using functorial virtual localization on certain moduli spaces of relative stable morphisms.
A tau function of the 2D Toda hierarchy can be obtained from a generating function of the two-partition cubic Hodge integrals. The associated Lax operators turn out to satisfy an algebraic relation. This algebraic relation can be used to…