I received my Ph.D. from the University of Georgia, USA, in May 2019. My advisor is Dan Nakano.

I am now a postdoc at Institute of Mathematics, Academia Sinica.

- Classification of spherical -distance -designs by solving Diophantine equations, joint work Eiichi Bannai, Etsuko Bannai, Wei-Hsuan Yu and Yan Zhu.
(PDF)

To appear in Taiwanese Journal of Mathematics.

Supplemental material: Mathematica code to solve a certain degree Diophantine equation in variables under some conditions. (Mathematica Notebook) (PDF) - Explicit spherical designs.
(PDF)

Submitted, Jul. 2018. - Rational designs, joint work with Zhen Cui and Jiacheng Xia.
(PDF)

Advances in Mathematics, 352, 541-571, 2019. doi:10.1016/j.aim.2019.06.012 - Nonexistence of nontrivial tight -designs.
(PDF)

Journal of Algebraic Combinatorics, 47(2), 301-318, 2018. doi:10.1007/s10801-017-0776-0 - A Fisher type inequality for weighted regular -wise balanced designs.
(PDF)

Journal of Combinatorial Theory A, 119(7), 1523-1527, 2012. doi:10.1016/j.jcta.2012.04.008

- The lit-only -game: some mathematics behind a puzzle for kids, joint work with Yaokun Wu.
(PDF)

The Mathematics Student, 88(3-4), 67-90, 2019. - Hamiltonian decomposition of prisms over cubic graphs, joint work with Moshe Rosenfeld,

Discrete Mathematics & Theoretical Computer Science, 16(2), 111-124, 2014.

- Integral points on variable separated curves, joint work with Dino Lorenzini. (PDF)

Sep. 2018.

- Chapter 4 of “Introduction to Soergel bimodules”,

to appear in the RSME Springer Series. - On -Schur algebras corresponding to Hecke algebras of type B, joint work with Chun-Ju Lai and Dan Nakano.
(PDF)

Submitted. Feb. 2019. - Support varieties for Hecke algebras, joint work with Dan Nakano.
(PDF)

Homology, Homotopy and Applications, 21(2), 59-82, 2019.

- Majorana representation of complex vectors, Temperley-Lieb category, and two variable hypergeometric series, joint work with Shaoshi Chen, Mikio Nakahara, Yan Zhu.
- New lower bound on the sizes of designs. (abstract)
- Hamiltonian thickness and spanning topological minors, joint work with Yaokun Wu and Yinfeng Zhu. (abstract)
- Lit-only -game, joint work with Yaokun Wu. (abstract)
- Inferring phylogenies from incomplete metric information, joint work with Yaokun Wu, Zeying Xu, Yinfeng Zhu.
- Positive matrices, primitive matrices, scrambling matrices and contractible matrices, joint work with Xinmao Wang and Yaokun Wu.
- Fiber products of P-polynomial association schemes. (abstract)
- On -distance sets in real hyperbolic space.

- Email: xiang@gate.sinica.edu.tw
- Email: xiang@ziqing.org
- Office: 624
- Mailing address:

Institute of Mathematics

Academia Sinica

6F, Astronomy-Mathematics Building

No. 1, Sec. 4, Roosevelt Road

Taipei 10617, Taiwan

- Combinatorics: Association Schemes, Design Theory, Graph Theory, Symbolic Dynamics, Phylogenetic combinatorics.
- Number Theory: Diophantine Equation, Finiteness of integral points, Variable separated curves.
- Representation Theory: Algebraic roups, Cohomology, Iwahori-Hecke Algebras, Quantum Groups, Schur Algebras.