15 citations · 95 across the 24 of their papers we have counts for
25 papers
Gromov-Witten Generating Series of Elliptic Curves as Configuration Space Integrals
Jie Zhou
The generating series of Gromov-Witten invariants of elliptic curves can be expressed in terms of multi-variable elliptic functions by works of Bloch-Okounkov and Okounkov-Pandhari…
Bi-Lipschitz Regularity of 2-Varifolds with the Critical Allard Condition
Yuchen Bi, Jie Zhou
For an intergral -varifold in the unit ball passing through the original point, assuming the critical Allard condition holds, that is, the a…
Twisted Sectors in Calabi-Yau Type Fermat Polynomial Singularities and Automorphic Forms
Dingxin Zhang, Jie Zhou
We study one-parameter deformations of Calabi-Yau type Fermat polynomial singularities along degree-one directions. We show that twisted sectors in the vanishing cohomology are com…
The sharp lower bound of the first Dirichlet eigenvalue for geodesic balls
Haibin Wang, Guoyi Xu, Jie Zhou
On complete noncompact Riemannian manifolds with non-negative Ricci curvature, Li-Schoen proved the uniform Poincare inequality for any ge odesic ball. In this note, we obtain the…
Gromov-Hausdorff convergence theory of surfaces
Sun Jianxin, Jie Zhou
In this paper, we use the viewpoint of Gromov-Haustorff convergence to give some new comprehension of well known theorem,it is Huber's classification theorem\cite{Huber}\cite{MS}fo…
Regularized Integrals on Riemann Surfaces and Modular Forms
Si Li, Jie Zhou
We introduce a simple procedure to integrate differential forms with arbitrary holomorphic poles on Riemann surfaces. It gives rise to an intrinsic regularization of such singular…
A genus-one FJRW invariant via two methods
Jun Li, Wei-Ping Li, Yefeng Shen +1
We calculate a genus-one FJRW invariant of an LG pair via two different methods. In the first method, we apply the cosection localization technique t…
Higher Genus FJRW Invariants of a Fermat Cubic
Jun Li, Yefeng Shen, Jie Zhou
We reconstruct the all-genus Fan-Jarvis-Ruan-Witten invariants of a Fermat cubic Landau-Ginzburg space $(x_1^3+x_2^3+x_3^3: [\mathbb{C}^3/ \mathboldμ_3]\to \mathbb{C})$ from genus-…
Topology of surfaces with finite Willmore energy
Jie Zhou
In this paper, we study the critical case of the Allard regularity theorem. Combining with Reifenberg's topological disk theorem, we get a critical Allard-Reifenberg type regularit…
Genus Two Quasi-Siegel Modular Forms and Gromov-Witten Theory of Toric Calabi-Yau Threefolds
Yongbin Ruan, Yingchun Zhang, Jie Zhou
We first develop theories of differential rings of quasi-Siegel modular and quasi-Siegel Jacobi forms for genus two. Then we apply them to the Eynard-Orantin topological recursion…
A Gromov-Hausdorff convergence theorem of surfaces in with small total curvature
Jianxin Sun, Jie Zhou
In this paper, we mainly study the compactness and local structure of immersing surfaces in with local uniform bounded area and small total curvature $\int_{Σ\cap B_…
Generating functions of planar polygons from homological mirror symmetry of elliptic curves
Kathrin Bringmann, Jonas Kaszian, Jie Zhou
We study generating functions of certain shapes of planar polygons arising from homological mirror symmetry of elliptic curves. We express these generating functions in terms of ra…
Open Gromov-Witten Theory of and Jacobi Forms
Bohan Fang, Yongbin Ruan, Yingchun Zhang +1
It was known through the efforts of many works that the generating functions in the closed Gromov-Witten theory of are meromorphic quasi-modular forms basing on t…
Genus one GW invariants of quintic threefolds via MSP localization
Huai-Liang Chang, Shuai Guo, Wei-Ping Li +1
The moduli stack of Mixed Spin P-fields (MSP) provides an effective algorithm to evaluate all genus Gromov-Witten invariants of quintic Calabi-Yau threefolds. This paper is to appl…
Mirror Symmetry for Plane Cubics Revisited
Jie Zhou
In this expository note we discuss some arithmetic aspects of the mirror symmetry for plane cubic curves. We also explain how the Picard-Fuchs equation can be used to reveal part o…
GKZ Hypergeometric Series for the Hesse Pencil, Chain Integrals and Orbifold Singularities
Jie Zhou
The GKZ system for the Hesse pencil of elliptic curves has more solutions than the period integrals. In this work we give different realizations and interpretations of the extra so…
LG/CY Correspondence for Elliptic Orbifold Curves via Modularity
Yefeng Shen, Jie Zhou
We prove the Landau-Ginzburg/Calabi-Yau correspondence between the Gromov-Witten theory of each elliptic orbifold curve and its Fan-Jarvis-Ruan-Witten theory counterpart via modula…
Airy Equation for the Topological String Partition Function in a Scaling Limit
Murad Alim, Shing-Tung Yau, Jie Zhou
We use the polynomial formulation of the holomorphic anomaly equations governing perturbative topological string theory to derive the free energies in a scaling limit to all orders…
Polynomial Structure of Topological String Partition Functions
Jie Zhou
We review the polynomial structure of the topological string partition functions as solutions to the holomorphic anomaly equations. We also explain the connection between the ring…
Modularity of Open Gromov-Witten Potentials of Elliptic Orbifolds
Siu-Cheong Lau, Jie Zhou
We study the modularity of the genus zero open Gromov-Witten potentials and its generating matrix factorizations for elliptic orbifolds. These objects constructed by Lagrangian Flo…
Ramanujan Identities and Quasi-Modularity in Gromov-Witten Theory
Yefeng Shen, Jie Zhou
We prove that the ancestor Gromov-Witten correlation functions of one-dimensional compact Calabi-Yau orbifolds are quasi-modular forms. This includes the pillowcase orbifold which…
Lectures on BCOV holomorphic anomaly equations
Atsushi Kanazawa, Jie Zhou
The present article surveys some mathematical aspects of the BCOV holomorphic anomaly equations introduced by Bershadsky, Cecotti, Ooguri and Vafa. It grew from a series of lecture…
Differential Rings from Special Kähler Geometry
Jie Zhou
We study triples of graded rings defined over the deformation spaces for certain one-parameter families of Calabi-Yau threefolds. These rings are analogues of the rings of modular…
Special Polynomial Rings, Quasi Modular Forms and Duality of Topological Strings
Murad Alim, Emanuel Scheidegger, Shing-Tung Yau +1
We study the differential polynomial rings which are defined using the special geometry of the moduli spaces of Calabi-Yau threefolds. The higher genus topological string amplitude…