Publications (93)
A Mathematical Theory of the Topological Vertex
Jun Li, Chiu-Chu Melissa Liu, Kefeng Liu +1
The $S^1$ fixed points in Quot-schemes and mirror principle computations
Bong H. Lian, Chien-Hao Liu, Kefeng Liu +1
Quasi-isometry and deformations of Calabi-Yau manifolds
Kefeng Liu, Sheng Rao, Xiaokui Yang
Modular invariance and anomaly cancellation formulas in odd dimension
Kefeng Liu, Yong Wang
A note on modular forms and generalized anomaly cancellation formulas
Kefeng Liu, Yong Wang
Computing top intersections in the tautological ring of $M_g$
Kefeng Liu, Hao Xu
Life-span of classical solutions to hyperbolic geometric flow in two space variables with slow decay initial data
De-Xing Kong, Kefeng Liu, Yu-Zhu Wang
Heat kernel and moduli spaces II
Kefeng Liu
Canonical Metrics on the Moduli Space of Riemann Surfaces II
Kefeng Liu, Xiaofeng Sun, Shing-Tung Yau
The n-point functions for intersection numbers on moduli spaces of curves
Kefeng Liu, Hao Xu
The hyperbolic geometric flow on Riemann surfaces
De-Xing Kong, Kefeng Liu, De-Liang Xu
Modular Forms and Generalized Anomaly Cancellation Formulas
Fei Han, Kefeng Liu, Weiping Zhang
Mariño-Vafa Formula and Hodge Integral Identities
Chiu-Chu Melissa Liu, Kefeng Liu, Jian Zhou
New structure for orthogonal quantum group invariants
Qingtao Chen, Kefeng Liu
Mean curvature flow of higher codimension in Riemannian manifolds
Kefeng Liu, Hongwei Xu, Entao Zhao
Effective vanishing theorems for ample and globally generated vector bundles
Kefeng Liu, Xiaokui Yang
Anomaly Cancellation and Modularity
Fei Han, Kefeng Liu, Weiping Zhang
Descendent integrals and tautological rings of moduli spaces of curves
Kefeng Liu, Hao Xu
Anomaly Cancellation and Modularity. II: $E_8\times E_8$ case
Fei Han, Kefeng Liu, Weiping Zhang
Curvatures of moduli space of curves and applications
Kefeng Liu, Xiaofeng Sun, Xiaokui Yang +1
Rigidity and Vanishing Theorems in K-Theory I
Kefeng Liu, Xiaonan Ma, Weiping Zhang
Topological String Partition Functions as Equivariant Indices
Jun Li, Kefeng Liu, Jian Zhou
Deforming submanifolds of arbitrary codimension in a sphere
Kefeng Liu, Hongwei Xu, Entao Zhao
A proof of the Faber intersection number conjecture
Kefeng Liu, Hao Xu
Congruent skein relations for colored HOMFLY-PT invariants and colored Jones polynomials
Qingtao Chen, Kefeng Liu, Pan Peng +1
Canonical Metrics on the Moduli Space of Riemann Surfaces I
Kefeng Liu, Xiaofeng Sun, Shing-Tung Yau
Volume conjecture for $SU(n)$-invariants
Qingtao Chen, Kefeng Liu, Shengmao Zhu
A geometric heat flow for vector fields
Yi Li, Kefeng Liu
Hyperbolic geometric flow (I): short-time existence and nonlinear stability
Wen-Rong Dai, De-Xing Kong, Kefeng Liu
New results of intersection numbers on moduli spaces of curves
Kefeng Liu, Hao Xu
New proofs of the Torelli theorems for Riemann surfaces
Kefeng Liu, Quanting Zhao, Sheng Rao
Rational curves on Hermitian manifolds
Huitao Feng, Kefeng Liu, Xueyuan Wan +1
Intersection numbers and automorphisms of stable curves
Kefeng Liu, Hao Xu
Localization, Hurwitz Numbers and the Witten Conjecture
Lin Chen, Yi Li, Kefeng Liu
Mirror Principle II
Bong H. Lian, Kefeng Liu, S. T. Yau
Mean Curvature Flow of Higher Codimension in Hyperbolic Spaces
Kefeng Liu, Hongwei Xu, Fei Ye +1
Mirror Principle IV
Bong H. Lian, Kefeng Liu, Shing-Tung Yau
A remark on weighted Bergman kernels on orbifolds
Xianzhe Dai, Kefeng Liu, Xiaonan Ma
A simple proof of Witten conjecture through localization
Yon-Seo Kim, Kefeng Liu
Boltje-Maisch resolutions of Specht modules
Xingyu Dai, Fang Li, Kefeng Liu
New Structure of Knot Invariants
Kefeng Liu, Pan Peng
Mathematical results inspired by physics
Kefeng Liu
Localization and Conjectures from String Duality
Kefeng Liu
Rigidity and Vanishing Theorems in K-Theory II
Kefeng Liu, Xiaonan Ma, Weiping Zhang
Proof of the Labastida-Marino-Ooguri-Vafa Conjecture
Kefeng Liu, Pan Peng
Ricci Curvatures on Hermitian manifolds
Kefeng Liu, Xiaokui Yang
A remark on 'Some numerical results in complex differential geometry'
Kefeng Liu, Xiaonan Ma
Modular Invariance and Characteristic Numbers
Kefeng Liu
On A-twisted moduli stack for curves from Witten's gauged linear sigma models
Chien-Hao Liu, Kefeng Liu, Shing-Tung Yau
Generalized Ricci flow I: Local existence and uniqueness
Chun-lei He, Sen Hu, De-Xing Kong +1
A Survey of Mirror Principle
Bong H. Lian, Kefeng Liu, Shing-Tung Yau
$K$-theory associated to vertex operator algebras
Chongying Dong, Kefeng Liu, Xiaonan Ma +1
Time-Periodic Solutions of the Einstein's Field Equations II
De-Xing Kong, Kefeng Liu, Ming Shen
Applications of the affine structures on the Teichmüller spaces
Kefeng Liu, Yang Shen, Xiaojing Chen
Curvatures of direct image sheaves of vector bundles and applications I
Kefeng Liu, Xiaokui Yang
Time-Periodic Solutions of the Einstein's Field Equations
De-Xing Kong, Kefeng Liu
Adiabatic Limits, Vanishing Theorems and the Noncommutative Residue
Kefeng Liu, Yong Wang
Finiteness of Subfamilies of Calabi-Yau n-Folds over Curves with Maximal Length of Yukawa-Coupling
Kefeng Liu, Andrey Todorov, Shing-Tung Yau +1
The extension and convergence of mean curvature flow in higher codimension
Kefeng Liu, Hongwei Xu, Fei Ye +1
Recent Development on the Geometry of the Teichmuller and Moduli Spaces of Riemann Surfaces and Polarized Calabi-Yau Manifolds
Kefeng Liu, Xiaofeng Sun, Shing-Tung Yau
An effective recursion formula for computing intersection numbers
Kefeng Liu, Hao Xu
On a Proof of a Conjecture of Marino-Vafa on Hodge Integrals
Chiu-Chu Melissa Liu, Kefeng Liu, Jian Zhou
Geometric Aspects of the Moduli Space of Riemann Surfaces
Kefeng Liu, Xiaofeng Sun, Shin-Tung Yau
A remark on Mirzakhani's asymptotic formulae
Kefeng Liu, Hao Xu
Adiabatic Limits and Foliations
Kefeng Liu, Weiping Zhang
Time-periodic universes
De-Xing Kong, Kefeng Liu, Ming Shen
On a proof of the Labastida-Marino-Ooguri-Vafa conjecture
Kefeng Liu, Pan Peng
Geometry of Hermitian manifolds
Kefeng Liu, Xiaokui Yang
On orbifold elliptic genus
Chongying Dong, Kefeng Liu, Xiaonan Ma
Gravitational Anomaly Cancellation and Modular Invariance
Fei Han, Kefeng Liu
Global Torelli Theorem for Teichmuller Spaces of Polarized Calabi-Yau manifolds
Kefeng Liu, Andrey Todorov, Xiaofeng Sun +1
A new kind of solutions of the Einstein's field equations with non-vanishing cosmological constant
De-Xing Kong, Kefeng Liu, Ming Shen
Hermitian Harmonic maps and non-degenerate curvatures
Kefeng Liu, Xiaokui Yang
Mirzakharni's recursion formula is equivalent to the Witten-Kontsevich theorem
Kefeng Liu, Hao Xu
Hyperbolic Mean Curvature Flow
Chun-Lei He, De-Xing Kong, Kefeng Liu
On Elliptic Genera and Foliations
Kefeng Liu, Xiaonan Ma, Weiping Zhang
$E_8$ Bundles and Rigidity
Fei Han, Kefeng Liu, Weiping Zhang
Elliptic genus and vertex operator algebras
Chongying Dong, Kefeng Liu, Xiaonan Ma
A Proof of a Conjecture of Marino-Vafa on Hodge Integrals
Chiu-Chu Melissa Liu, Kefeng Liu, Jian Zhou
Positivity and vanishing theorems for ample vector bundles
Kefeng Liu, Xiaofeng Sun, Xiaokui Yang
Remarks on the Chern classes of Calabi-Yau moduli
Kefeng Liu, Changyong Yin
A Basis of the $q$-Schur Module
Xingyu Dai, Fang Li, Kefeng Liu
$S^1$-fixed-points in hyper-Quot-schemes and an exact mirror formula for flag manifolds from the extended mirror principle diagram
Chien-Hao Liu, Kefeng Liu, Shing-Tung Yau
Quantum Correction and the Moduli Spaces of Calabi-Yau Manifolds
Kefeng Liu, Changyong Yin
Shafarevich's Conjecture for CY Manifolds I
Kefeng Liu, Andrey Todorov, Shing-Tung Yau +1
New properties of the intersection numbers on moduli spaces of curves
Kefeng Liu, Hao Xu
Hyperbolic mean curvature flow: Evolution of plane curves
De-Xing Kong, Kefeng Liu, Zeng-Gui Wang
A Formula of Two-Partition Hodge Integrals
Chiu-Chu Melissa Liu, Kefeng Liu, Jian Zhou
Recursion formulae of higher Weil-Petersson volumes
Kefeng Liu, Hao Xu
Formal pseudodifferential operators and Witten's r-spin numbers
Kefeng Liu, Ravi Vakil, Hao Xu
Remarks on the Cartan Formula and Its Applications
Kefeng Liu, Sheng Rao
Heat kernels, symplectic geometry, moduli spaces and finite groups
Kefeng Liu
Dissipative Hyperbolic Geometric Flow
Wen-Rong Dai, De-Xing Kong, Kefeng Liu