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Home || Talks || CV

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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) (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 \(8\)-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 \(t\)-wise balanced designs. (PDF)
  Journal of Combinatorial Theory A, 119(7), 1523-1527, 2012. doi:10.1016/j.jcta.2012.04.008

Graph Theory

• The lit-only \(\sigma\)-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.

Number Theory

• Integral points on variable separated curves, joint work with Dino Lorenzini. (PDF)
  Sep. 2018.

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. (PDF)
  Transformation Groups, 2020. doi:10.1007/s00031-020-09628-7
• Support varieties for Hecke algebras, joint work with Dan Nakano. (PDF)
  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.

Contact

• 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.