56 citations · 642 across the 79 of their papers we have counts for
37 papers · 1 filter
K-Theory of Hilbert Schemes as a Formal Quantum Field Theory
Jian Zhou
We define a notion of formal quantum field theory and associate a formal quantum field theory to K-theoretical intersection theories on Hilbert schemes of points on algebraic surfa…
On Quasimodularity of Some Equivariant Intersection Numbers on the Hilbert Schemes
Jian Zhou
We observe that certain equivariant intersection numbers of Chern characters of tautological sheaves on Hilbert schemes for suitable circle actions can be computed using the Bloch-…
On Equivariant Elliptic Genera of Toric Calabi-Yau 3-folds
Jian Zhou
We show that equivariant elliptic genera of toric Calabi-Yau 3-folds are generalized weak Jacobi forms. We also introduce a notion of averaged equivariant elliptic genera of toric…
On a Mean Field Theory of Topological 2D Gravity
Jian Zhou
We present a one-dimensional mean field theory for topological 2D gravity. We discuss possible generalizations to other topological field theories, in particular those related to s…
Quantum Deformation Theory of the Airy Curve and Mirror Symmetry of a Point
Jian Zhou
We present a quantum deformation theory of the Airy curve and use it to establish a version of mirror symmetry of a point.
Explicit Formula for Witten-Kontsevich Tau-Function
Jian Zhou
We present an explicit formula for Witten-Kontsevich tau-function.
Gopakumar-Vafa BPS invariants, Hilbert schemes and quasimodular forms. I
Shuai Guo, Jian Zhou
We prove a closed formula for leading Gopakumar- Vafa BPS invariants of local Calabi-Yau geometries given by the canonical line bundles of toric Fano surfaces. It shares some simil…
Quantum Mirror Curves for and the Resolved Confiold
Jian Zhou
We establish a conjecture of Gukov and Sułkowski in the following three cases: Lambert curve for Hurwitz numbers, framed mirror curve of , and the framed mirror curv…
Intersection numbers on Deligne-Mumford moduli spaces and quantum Airy curve
Jian Zhou
We establish the Airy curve case of a conjecture of Gukov and Sułkowski by reducing to Dijkgraaf-Verlinde-Verlinde Virasoro constraints satisfied by the intersection numbers on mod…
Fermionic gluing principle of the topological vertex
Fusheng Deng, Jian Zhou
We will establish the fermionic gluing principle of the topological vertex, that is, provided the framed ADKMV conjecture, the generating functions of the Gromov-Witten invariants…
On fermionic representation of the Gromov-Witten invariants of the resolved Conifold
Fusheng Deng, Jian Zhou
We prove that the fermionic form of the generating function of the Gromov-Witten invariants of the resolved conifold is a Bogoliubov transform of the fermionic vacuum; in particula…
On fermionic representation of the framed topological vertex
Fusheng Deng, Jian Zhou
The Gromov-Witten invariants of \mathbb{C}^3 with branes is encoded in the topological vertex which has a very complicated combinatorial expression. A simple formula for the topolo…
Integrality Properties of Open-Closed Mirror Maps
Jian Zhou
We propose a conjecture on integrality property of the open-closed mirror maps of compact Calabi-Yau manifolds. Some examples are presented.
Integrality Properties of Variations of Mahler Measures
Jian Zhou
We propose some conjectures on the integrality properties related to the variation of Mahler measures, inspired by the results in the elliptic curve case by Rodriguez Villegas, Sti…
Some integrality properties in local mirror symmetry
Jian Zhou
We prove some integrality properties of the open-closed mirror maps, inverse open-closed mirror maps and mirror curves of some local Calabi-Yau geometries.
A Proof of the Full Marino-Vafa Conjecture
Jian Zhou
We present a proof of the full Mariño-Vafa Conjecture that identifies certain open string invariants of the resolved conifold with the Chern-Simons knot invariant of the unknot, i.…
Open String Invariants and Mirror Curve of the Resolved Conifold
Jian Zhou
For the resolved conifold with one outer D-brane in arbitrary framing, we present some results for the open string partition functions obtained by some operator manipulations. We p…
Local Mirror Symmetry for the Topological Vertex
Jian Zhou
For three-partition triple Hodge integrals related to the topological vertex, we derive Eynard-Orantin type recursion relations from the cut-and-join equation. This establishes a v…
Local Mirror Symmetry for One-Legged Topological Vertex
Jian Zhou
We prove the Bouchard-Mariño Conjecture for the framed one-legged topological vertex by deriving the Eynard-Orantin type recursion relations from the cut-and-join equation satisfie…
Crepant Resolutions, Quivers and GW/NCDT Duality
Jian Zhou
We propose a conjecture that relates some local Gromov-Witten invariants of some crepant resolutions of Calabi-Yau 3-folds with isolated singularities with some Donaldson-Thomas ty…
Arithmetic McKay correspondence
Jian Zhou
We propose an arithmetic McKay correspondence which relates suitably defined zeta functions of some Deligne-Mumford stacks to the zeta functions of their crepant resolutions. Some…
Crepant resolution conjecture in all genera for type A singularities
Jian Zhou
We prove an all genera version of the Crepant Resolution Conjecture of Ruan and Bryan-Graber for type A surface singularities. We are based on a method that explicitly computes Hur…
On computations of Hurwitz-Hodge integrals
Jian Zhou
We describe a method to compute Hurwitz-Hodge integrals.
On a deformed topological vertex
Jian Zhou
We introduce a deformed topological vertex and use it to define deformations of the topological string partition functions of some local Calabi-Yau geometries. We also work out som…