百晓学者学者目录

张友金

教授、讲师，清华大学

精选作品

期刊论文

2026

The Extended Ablowitz–Ladik Hierarchy and a Generalized Frobenius Manifold

Siqi Liu, Yuewei Wang, Youjin Zhang

Communications in Mathematical Physics

DOI

2026

Generalized Frobenius manifold structures on the orbit spaces of affine Weyl groups II

Lingrui Jiang, Si-qi Liu, Yingchao Tian, Youjin Zhang

Journal of Geometry and Physics

DOI

2025

Legendre Transformations of a Class of Generalized Frobenius Manifolds and the Associated Integrable Hierarchies

Siqi Liu, Haonan Qu, Youjin Zhang

Communications in Mathematical Physics

DOI

2025

Generalized Frobenius Manifolds with Non-flat Unity and Integrable Hierarchies

Siqi Liu, Haonan Qu, Youjin Zhang

Communications in Mathematical Physics

DOI

2025

On tautological flows of partial difference equations

Zhonglun Cao, Siqi Liu, Youjin Zhang

Physica D Nonlinear Phenomena

DOI

2024

Linearization of Virasoro symmetries associated with semisimple Frobenius manifolds

Siqi Liu, Zhe Wang, Youjin Zhang

Advances in Mathematics

DOI

2024

Solutions of the Loop Equations of a Class of Generalized Frobenius Manifolds

Siqi Liu, Haonan Qu, Yuewei Wang, Youjin Zhang

Communications in Mathematical Physics

DOI

2023

Variational Bihamiltonian Cohomologies and Integrable Hierarchies III: Linear Reciprocal Transformations

Siqi Liu, Zhe Wang, Youjin Zhang

Communications in Mathematical Physics

DOI

2023

Variational Bihamiltonian Cohomologies and Integrable Hierarchies I: Foundations

Siqi Liu, Zhe Wang, Youjin Zhang

Communications in Mathematical Physics

DOI

2022

Variational Bihamiltonian Cohomologies and Integrable Hierarchies II: Virasoro Symmetries

Siqi Liu, Zhe Wang, Youjin Zhang

Communications in Mathematical Physics

DOI

2022

Reduction of the 2D Toda Hierarchy and Linear Hodge Integrals

Siqi Liu, Zhe Wang, Youjin Zhang

Symmetry Integrability and Geometry Methods and Applications

DOI

2022

The Virasoro-Like Algebra of a Frobenius Manifold

Siqi Liu, Di Yang, Youjin Zhang, Jian Zhou

International Mathematics Research Notices

DOI

2022

The loop equation for special cubic Hodge integrals

Siqi Liu, Di Yang, Youjin Zhang, Chunhui Zhou

Journal of Differential Geometry

DOI

2022

Virasoro constraints for Drinfeld–Sokolov hierarchies and equations of Painlevé type

Siqi Liu, Chao‐Zhong Wu, Youjin Zhang

Journal of the London Mathematical Society

DOI

2022

Tri-Hamiltonian structure of the Ablowitz–Ladik hierarchy

Shuangxing Li, Siqi Liu, Haonan Qu, Youjin Zhang

Physica D Nonlinear Phenomena

DOI

2021

Super tau-covers of bihamiltonian integrable hierarchies

Siqi Liu, Zhe Wang, Youjin Zhang

Journal of Geometry and Physics

DOI

2021

The Hodge-FVH correspondence

Siqi Liu, Di Yang, Youjin Zhang, Chunhui Zhou

Journal für die reine und angewandte Mathematik (Crelles Journal)

DOI

2020

Hodge–GUE Correspondence and the Discrete KdV Equation

Boris Anatol'evich Dubrovin, Siqi Liu, Di Yang, Youjin Zhang

Communications in Mathematical Physics

DOI

2020

Masur–Veech volumes of quadratic differentials and their asymptotics

Di Yang, Don Bernard Zagier, Youjin Zhang

Journal of Geometry and Physics

DOI

2019

Drinfeld–Sokolov Hierarchies and Diagram Automorphisms of Affine Kac–Moody Algebras

Siqi Liu, Chao‐Zhong Wu, Youjin Zhang, Xu Zhou

Communications in Mathematical Physics

DOI

2019

Extended affine Weyl groups of BCD-type: Their Frobenius manifolds and Landau–Ginzburg superpotentials

Boris Anatol'evich Dubrovin, Ian A. B. Strachan, Youjin Zhang, Dafeng Zuo

Advances in Mathematics

DOI

2017

Fractional Volterra hierarchy

Siqi Liu, Youjin Zhang, Chunhui Zhou

Letters in Mathematical Physics

DOI

2016

Hodge integrals and tau-symmetric integrable hierarchies of Hamiltonian evolutionary PDEs

Boris Anatol'evich Dubrovin, Siqi Liu, Di Yang, Youjin Zhang

Advances in Mathematics

DOI

2015

Central invariants of the constrained KP hierarchies

Siqi Liu, Youjin Zhang, Xu Zhou

Journal of Geometry and Physics

DOI

2014

BCFG Drinfeld–Sokolov hierarchies and FJRW-theory

Siqi Liu, Yongbin Ruan, Youjin Zhang

Inventiones mathematicae

DOI

2013

Bihamiltonian Cohomologies and Integrable Hierarchies I: A Special Case

Siqi Liu, Youjin Zhang

Communications in Mathematical Physics

DOI

2013

Proof of a conjecture on the genus two free energy associated to the An singularity

Yulong Fu, Siqi Liu, Youjin Zhang, Chunhui Zhou

Journal of Geometry and Physics

DOI

2013

Recent development in symmetries and integrability of difference equations

Xing‐Biao Hu, Qingping Liu, Sen‐Yue Lou, Changzheng Qu, Youjin Zhang

Frontiers of Mathematics

DOI

2012

The inversion symmetry of the WDVV equations and tau functions

Siqi Liu, Dingdian Xu, Youjin Zhang

Physica D Nonlinear Phenomena

DOI

2009

Hamiltonian structures and their reciprocal transformations for the r -KdV–CH hierarchy

Ming Chen, Siqi Liu, Youjin Zhang

Journal of Geometry and Physics

DOI

2008

Frobenius manifolds and central invariants for the Drinfeld–Sokolov bihamiltonian structures

Boris Anatol'evich Dubrovin, Siqi Liu, Youjin Zhang

Advances in Mathematics

DOI

2008

On Properties of Hamiltonian Structures for a Class of Evolutionary PDEs

Siqi Liu, Chao‐Zhong Wu, Youjin Zhang

Letters in Mathematical Physics

DOI

2006

A Two-component Generalization of the Camassa-Holm Equation and its Solutions

Ming Chen, Si‐Qi Liu, Youjin Zhang

Letters in Mathematical Physics

DOI

2006

On quasi-triviality and integrability of a class of scalar evolutionary PDEs

Siqi Liu, Youjin Zhang

Journal of Geometry and Physics

DOI

2005

On Hamiltonian perturbations of hyperbolic systems of conservation laws I: Quasi‐Triviality of bi‐Hamiltonian perturbations

Boris Anatol'evich Dubrovin, Si‐Qi Liu, Youjin Zhang

Communications on Pure and Applied Mathematics

DOI

2004

Deformations of semisimple bihamiltonian structures of hydrodynamic type

Siqi Liu, Youjin Zhang

Journal of Geometry and Physics

DOI

2002

On the CP1 topological sigma model and the Toda lattice hierarchy

Youjin Zhang

Journal of Geometry and Physics

DOI

2002

Deformations of the Bihamiltonian Structures on the Loop Space of Frobenius Manifolds

Youjin Zhang

Journal of Nonlinear Mathematical Physics

DOI

预印本

2026

Finite Group Reduction of the DR/DZ Hierarchies

Si-Qi Liu, Youjin Zhang, Tianwen Zhong

arXiv preprint

2025

Generalized Frobenius Manifold Structures on the Orbit Spaces of Affine Weyl Groups I

Lingrui Jiang, Si-Qi Liu, Yingchao Tian, Youjin Zhang

arXiv preprint

2025

On a class of integrable deformations of the integrable hierarchy of topological type associated to a semisimple Frobenius manifold

Si-Qi Liu, Paolo Rossi, Di Yang, Youjin Zhang

arXiv preprint

2017

Bihamiltonian Cohomologies and Integrable Hierarchies II: the Tau Structures

Boris Dubrovin, Si-Qi Liu, Youjin Zhang

arXiv preprint

DOI

2013

Uniqueness Theorem of W-Constraints for Simple Singularities

Si-Qi Liu, Di Yang, Youjin Zhang

arXiv preprint

DOI

2012

On the Genus Two Free Energies for Semisimple Frobenius Manifolds

Boris Dubrovin, Si-Qi Liu, Youjin Zhang

arXiv preprint

DOI

2010

On Symmetries of the WDVV Equations

Dingdian Xu, Youjin Zhang

arXiv (Cornell University)

DOI

2009

Jacobi Structures of Evolutionary Partial Differential Equations

Si-Qi Liu, Youjin Zhang

arXiv preprint

2009

On the Drinfeld-Sokolov Hierarchies of D type

Si-Qi Liu, Chao-Zhong Wu, Youjin Zhang

arXiv preprint

2008

Virasoro Symmetries of the Extended Toda Hierarchy

Boris Anatol'evich Dubrovin, Youjin Zhang

2005

Bihamiltonian Systems of Hydrodynamic Type and Reciprocal Transformations

Ting Xue, Youjin Zhang

2005

Extended affine Weyl groups and Frobenius manifolds -- II

Boris Dubrovin, Youjin Zhang, Dafeng Zuo

arXiv preprint

2003

The Extended Toda Hierarchy

Guido Carlet, Boris Dubrovin, Youjin Zhang

arXiv preprint

2001

Normal forms of hierarchies of integrable PDEs, Frobenius manifolds and Gromov - Witten invariants

Boris Dubrovin, Youjin Zhang

arXiv preprint

1998

Frobenius Manifolds And Virasoro Constraints

Boris Dubrovin, Youjin Zhang

arXiv preprint

1997

Bihamiltonian Hierarchies in 2D Topological Field Theory At One-Loop Approximation

Boris Dubrovin, Youjin Zhang

arXiv preprint

DOI

1996

Extended affine Weyl groups and Frobenius manifolds

Boris Dubrovin, Youjin Zhang

arXiv preprint

书籍章节

2022

On equivariant Gromov–Witten invariants of resolved conifold with diagonal and anti-diagonal actions

Siqi Liu, Di Yang, Youjin Zhang, Chunhui Zhou

Letters in Mathematical Physics

DOI

研究方向

数学物理可积系统理论

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