A description of my research.
Combinatorics: Eulerian Structure
- Linear Conditions on the Number of Faces of Manifolds with Boundary. (with B.F. Chen)
Advances in Applied Mathematics 19 (1997) 144-168. pdf - f-Vectors of Polyhedra.
Geometriae Dedicata 68 (1997) 21-28. pdf - The Geometric Cone Relations for Simplicial and Cubical Complexes. (with B.F. Chen)
Discrete Mathematics 183 (1998) 39-46. pdf - Eulerian Stratification of Polyhedra. (with B.F. Chen)
Advances in Applied Mathematics 21 (1998) 22-57. pdf - Singularities from Eulerian Viewpoint. (with B.F. Chen)
Proceedings of the Steklov Institute of Mathematics 221 (1998) 305-319. pdf - Eulerian 2-Strata Spaces. (with B.F. Chen)
Journal of Combinatorial Theory, Series A 85 (1999) 1-28. pdf
Combinatorics: Spherical Tilings by Pentagons
- Spherical Tiling by 12 Congruent Pentagons. (with H.H. Gao and N. Shi)
Journal of Combinatorial Theory, Series A 120 (2013) 744-776. arXiv - Combinatorial Tilings of the Sphere by Pentagons.
Electronic Journal of Combinatorics 20 (2013) P54. arXiv - Tilings of the Sphere by Edge Congruent Pentagons. (with K.Y. Cheuk and H.M. Cheung)
preprint. arXiv - Tilings of the Sphere by Geometrically Congruent Pentagons I. (with K.Y. Cheuk and H.M. Cheung)
preprint. arXiv - Angle Combinations in Spherical Tilings by Congruent Pentagons. (with H.P. Luk)
preprint. arXiv
Hopf Algebra
- Stabilizer for Hopf Algebra Actions. (with Y.C. Zhu)
Communications in Algebra 26 (1998) 3885-3898. pdf - Quasi-triangular Structures on Hopf Algebra with a Positive Basis. (with J.H. Lu and Y.C. Zhu)
In New Trends in Hopf Algebra Theory, 339-356, Contemporary Mathematics 267, AMS Press 2000. pdf - On the Set-theoretical Yang-Baxter Equation. (with J.H. Lu and Y.C. Zhu)
Duke Mathematical Journal 104 (2000) 1-18. pdf - On Hopf Algebras with Positive Bases. (with J.H. Lu and Y.C. Zhu)
Journal of Algebra 237 (2001) 421-445. pdf
Integrable System: Painlevé Test
- Singularity Analysis for Integrable Systems by Their Mirrors. (with J.S. Hu)
Nonlinearity 12 (1999) 1531-1543. pdf - The Mirror Systems of Integrable Equations. (with J.S. Hu)
Studies in Applied Mathematics 104 (2000) 67-90. pdf - Local Analyticity of Solutions in the Painlevé Test. (with J.S. Hu)
In Proceedings of the Workshop on Nonlinearity, Integrability and All That: Twenty Years after NEEDS '79, 146-152, World Scientific 2000. - Symplectic Structure of the Painlevé Test. (with J.S. Hu)
Journal of Nonlinear Mathematical Physics 8 (2001) 145-148. pdf - Mirror Transforms of Hamiltonian Systems. (with J.S. Hu and T.L. Yee)
Physica D 152-153 (2001) 110-123. pdf - A Link between two Fundamental Contributions of Kowalevski. (with J.S. Hu)
In The Kowalevski Property, CRM Proceedings & Lecture Notes, 146-152, AMS Press 2002. pdf - An Elementary and Direct Proof of the Painlevé Property for the Painlevé Equations I, II and IV. (with J.S. Hu)
Journal d'Analyse Mathématique 91 (2003) 105-121. pdf - Painlevé Test and the Resolution of Singularities for Integrable Equations. (with J.S. Hu)
preprint. arXiv
Topology: Equivariant Surgery
- The Periodicity in Stable Equivariant Surgery.
Communications on Pure and Applied Mathematics 46 (1993) 1013-1040. pdf - Equivariant Periodicity in Surgery for Actions of Some Nonabelian Groups.
In Proceedings of 1993 Georgia Topology Conference, 478-508, AMS and International Press 1997. pdf - Equivariant Periodicity for Abelian Group Actions. (with S. Weinberger)
Advances in Geometry 1 (2001) 49-70. pdf - Equivariant Periodicity for Compact Group Actions. (with S. Weinberger)
Advances in Geometry 5 (2005) 363-376. pdf - Replacement Theorems for Compact Group Actions: The 2ρ Theorem. (with S. Cappell and S. Weinberger)
Pure and Applied Mathematics Quarterly 8 (2012) 53-78. arXiv - Closed Aspherical Manifolds with Center. (with S. Cappell and S. Weinberger)
to appear in Journal of Topology. arXiv - Topological Classification of Multiaxial U(n)-Actions. (with S. Cappell and S. Weinberger)
submitted. arXiv - Functoriality of Isovariant Homotopy Classification. (with S. Cappell and S. Weinberger)
preprint. arXiv
Miscellaneous