# Weiqiang HeSun Yat-Sen University | SYSU · Department of Mathematics

Weiqiang He

Doctor of Philosophy

## About

16

Publications

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57

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Introduction

**Skills and Expertise**

## Publications

Publications (16)

A new version of preprint has been updated. Argement is fully simplified, some gap are fixed, and a discussion on quantum hikita conjecture is added. Comments are welcomed.
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...

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...

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...

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)...

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...

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...

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...

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.

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...

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...

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.

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.

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.

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.

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.