Weiqiang He

Weiqiang He
Sun Yat-Sen University | SYSU · Department of Mathematics

Doctor of Philosophy

About

16
Publications
908
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53
Citations
Citations since 2017
12 Research Items
41 Citations
201720182019202020212022202302468
201720182019202020212022202302468
201720182019202020212022202302468
201720182019202020212022202302468

Publications

Publications (16)
Preprint
Full-text available
We show that the equivariant cohomology ring of the minimal resolution of an ADE singularity is isomorphic to the $B$-algebra of the quantization of the coordinate ring of the minimal nilpotent orbit in the Lie algebra of the same type. This generalizes a recent result of Shlykov [Hikita conjecture for the minimal nilpotent orbit,arXiv:1903.12205]...
Preprint
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We study the Dubrovin-Frobenius manifold in the Fan-Jarvis-Ruan-Witten theory of Landau-Ginzburg pairs $(W, )$, where $W$ is an invertible nondegenerate quasihomogeneous polynomial with two variables and $ $ is a minimal admissible group of $W$. We conjecture that the Dubrovin-Frobenius manifolds from these FJRW theory are semisimple. We prove the...
Article
For an invertible quasihomogeneous polynomial 𝒘 {{\boldsymbol{w}}} we prove an all-genus mirror theorem relating two cohomological field theories of Landau–Ginzburg type. On the B -side it is the Saito–Givental theory for a specific choice of a primitive form. On the A -side, it is the matrix factorization CohFT for the dual singularity 𝒘 T {{\bold...
Preprint
Full-text available
We introduce Virasoro operators in quantum singularity theories for non-degenerate quasi-homogeneous polynomials with certain group of diagonal symmetries. We conjecture that the total ancestor potentials constructed in quantum singularity theories are annihilated by these Virasoro operators. We prove the conjecture in various cases, including: (1)...
Article
Full-text available
We explain how dispersionless integrable hierarchy in 2d topological field theory arises from the Kodaira–Spencer gravity (BCOV theory). The infinitely many commuting Hamiltonians are given by the current observables associated to the infinite abelian symmetries of the Kodaira–Spencer gravity. We describe a BV framework of effective field theories...
Article
In this paper we report some explicit evolutionary PDEs of the Drinfeld-Sokolov hierarchy of type \(E_6^{(1)}\), and show how the unknown functions in these PDEs are related to the tau function. Moreover, for this hierarchy we compute its topological solution of formal series up to a certain degree, whose coefficients of monomials give the Fan-Jarv...
Preprint
Full-text available
For an in invertible quasihomogeneous singularity $w$ we prove an all-genus mirror theorem establishing an isomorphism between two cohomological field theories. On the $B$-side it is the Saito-Givental theory given by a certain choice of a primitive form. On the $A$-side, it is the reduced matrix factorization CohFT for the dual singularity $w^T$ w...
Article
Full-text available
Given an algebra with group $G$-action, we construct brace structures for its $G$-twisted Hochschild cochains. An an application, we construct $G$-Frobenius algebras for orbifold Landau-Ginzburg B-models and present explicit orbifold cup product formula for all invertible polynomials.
Preprint
Full-text available
We explain how dispersionless integrable hierarchy in 2d topological field theory arises from the Kodaira-Spencer gravity (BCOV theory). The infinitely many commuting Hamiltonians are given by the current observables associated to the infinite abelian symmetries of the Kodaira-Spencer gravity. We describe a BV framework of effective field theories...
Preprint
Full-text available
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-Manin connection to Hochschild chains twisted by group action. As an application, we provide explicit computations for the Getzler-Gauss-Manin connection on the universal (n...
Article
Full-text available
Using the degeneration formula and absolute/relative correspondence, we study the change of Gromov–Witten invariants under blow-ups for smooth projective threefolds, and obtain several closed blow-up formulae for high genus Gromov–Witten invariants. Our formulae also imply some simple relations among generalized BPS numbers.
Article
Full-text available
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 symplectic orbifolds is proved. These results extend the results of manifolds case to orbifold case.
Article
Full-text available
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-model) of such a polynomial is equivalent to the Saito-Givental theory (LG B-model) of the mirror polynomial.
Article
Full-text available
Using the degeneration formula and localization technique, one studied the change of high genus Gromov-Witten invariants under the blowup for six dimensional symplectic manifolds and obtained a close blow-up formula for any genus Gromov-Witten invariants.
Article
Full-text available
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 symplectic orbifolds is proved. These results extend the results of manifolds case to orbifold case.

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