17 citations · 31 across the 12 of their papers we have counts for
12 papers
Cluster algebras and quantum cohomology rings: A-type
Weiqiang He, Yingchun Zhang
We construct a cluster algebra structure within the quantum cohomology ring of a quiver variety associated with an -type quiver. Specifically, let d…
Quantization of the minimal nilpotent orbits and the quantum Hikita conjecture
Xiaojun Chen, Weiqiang He, Sirui Yu
We show that the specialized quantum D-module of the equivariant quantum cohomology ring of the minimal resolution of an ADE singularity is isomorphic to the D-module of graded tra…
Semisimple FJRW theory of polynomials with two variables
Amanda Francis, Weiqiang He, Yefeng Shen
We study the Dubrovin-Frobenius manifold in the Fan-Jarvis-Ruan-Witten theory of Landau-Ginzburg pairs $(W, \<J\>)$, where is an invertible nondegenerate quasihomogeneous polyn…
Seiberg Duality conjecture for star-shaped quivers and finiteness of Gromov-Witten thoery for D-type quivers
Weiqiang He, Yingchun Zhang
This is the second work on Seiberg Duality. This work proves that the Seiberg duality conjecture holds for star-shaped quivers: the Gromov-Witten theories for two mutation-related…
Virasoro constraints in quantum singularity theories
Weiqiang He, Yefeng Shen
We introduce Virasoro operators for any Landau-Ginzburg pair (W, G) where W is a non-degenerate quasi-homogeneous polynomial and G is a certain group of diagonal symmetries. We pro…
A Landau-Ginzburg mirror theorem via matrix factorizations
Weiqiang He, Alexander Polishchuk, Yefeng Shen +1
For an in invertible quasihomogeneous singularity we prove an all-genus mirror theorem establishing an isomorphism between two cohomological field theories. On the -side it…
Dispersionless Integrable Hierarchy via Kodaira-Spencer Gravity
Weiqiang He, Si Li, Xinxing Tang +1
We explain how dispersionless integrable hierarchy in 2d topological field theory arises from the Kodaira-Spencer gravity (BCOV theory). The infinitely many commuting Hamiltonians…
Unfolding of Orbifold LG B-Models: A Case Study
Weiqiang He, Si Li, Yifan Li
In this note we explore the variation of Hodge structures associated to the orbifold Landau-Ginzburg B-model whose superpotential has two variables. We extend the Getzler-Gauss-Man…
G-twisted braces and orbifold Landau-Ginzburg Models
Weiqiang He, Si Li, Yifan Li
Given an algebra with group -action, we construct brace structures for its -twisted Hochschild cochains. An an application, we construct -Frobenius algebras for orbifold L…
Landau-Ginzburg Mirror Symmetry Conjecture
Weiqiang He, Si Li, Yefeng Shen +1
We prove the Landau-Ginzburg mirror symmetry conjecture between invertible quasi-homogeneous polynomial singularities at all genera. That is, we show that the FJRW theory (LG A-mod…
Blow-up formulae of high genus Gromov-Witten invariants in dimensional six
Weiqiang He, Jianxun Hu, Hua-Zhong Ke +1
Using the degeneration formula and absolute/relative correspondence, one studied the change of Gromov-Witten invariants under blow-up for six dimensional symplectic manifolds and o…
Orbifold Gromov-Witten Invariants of Weighted Blow-up at Smooth Points
Weiqiang He, Jianxun Hu
In this paper, one considers the change of orbifold Gromov-Witten invariants under weighted blow-up at smooth points. Some blow-up formula for Gromov-Witten invariants of symplecti…