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