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Ziqing Xiang
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. My host is Ching Hung Lam.
Algebraic Combinatorics
- Classification of spherical \(2\)-distance \(\{4, 2, 1\}\)-designs by solving Diophantine equations, joint work Eiichi Bannai, Etsuko Bannai, Wei-Hsuan Yu and Yan Zhu.
(PDF)
Taiwanese Journal of Mathematics. doi:10.11650/tjm/200601
Supplemental material: Mathematica code to solve a certain degree \(10\) Diophantine equation in \(3\) variables under some conditions.
(Mathematica Notebook)
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- Explicit spherical designs.
(PDF)
Submitted, Jul. 2018.
- Rational designs, joint work with Zhen Cui and Jiacheng Xia.
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Advances in Mathematics, 352, 541-571, 2019.
doi:10.1016/j.aim.2019.06.012
- Nonexistence of nontrivial tight \(8\)-designs.
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Journal of Algebraic Combinatorics, 47(2), 301-318, 2018.
doi:10.1007/s10801-017-0776-0
- A Fisher type inequality for weighted regular \(t\)-wise balanced designs.
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Journal of Combinatorial Theory A, 119(7), 1523-1527, 2012.
doi:10.1016/j.jcta.2012.04.008
Graph Theory
Number Theory
Representation Theory
- Chapter 4 of “Introduction to Soergel bimodules” by Ben Elias, Shotaro Makisumi, Ulrich Thiel, Geordie Williamson,
RSME Springer Series 5, 2020. doi:10.1007/978-3-030-48826-0
- On \(q\)-Schur algebras corresponding to Hecke algebras of type B, joint work with Chun-Ju Lai and Dan Nakano.
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Transformation Groups, 2020. doi:10.1007/s00031-020-09628-7
- Support varieties for Hecke algebras, joint work with Dan Nakano.
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Homology, Homotopy and Applications, 21(2), 59-82, 2019. doi:10.4310/HHA.2019.v21.n2.a5
Papers in preparation
- Majorana representation of complex vectors, Temperley-Lieb category, and two variable hypergeometric series, joint work with Shaoshi Chen, Mikio Nakahara, Yan Zhu.
- Finiteness of tight combinatorial designs.
- 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 \(\sigma\)-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 \(s\)-distance sets in real hyperbolic space.
- Hyperbolicity of the product graphs.
- 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
Research Interests
- 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.