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Ziqing Xiang

I am a fifth year graduate student at University of Georgia, USA. My advisor is Dan Nakano.

I am on the job market this year. My research statement is available here.

Algebraic Combinatorics

• Classification of spherical $2$-distance $\{4, 2, 1\}$-design, joint work Eiichi Bannai, Etsuko Bannai, Wei-Hsuan Yu and Yan Zhu, Submitted, Aug. 2018. (PDF)
  Supplemental material: Mathematica code to solve a certain degree $10$ Diophantine equation in $3$ variables under some conditions. (Mathematica Notebook) (PDF)
• Explicit spherical designs. Submitted, Jul. 2018. (PDF)
• Rational designs, joint work with Zhen Cui and Jiacheng Xia. Submitted, Oct. 2017. (PDF)
• 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
• Nonexistence of nontrivial tight $8$-designs, (PDF)
  Journal of Algebraic Combinatorics, 47(2), 301-318, 2018. doi:10.1007/s10801-017-0776-0

Graph Theory

• 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. Sep. 2018. (PDF)

Representation Theory

• Support varieties for Hecke algebras, joint work with Dan Nakano,
  Homology, Homotopy and Applications, accepted. (PDF)

Papers in preparation

• On $q$-Schur algebras corresponding to Hecke algebras of type B, joint work with Chun-Ju Lai and Dan Nakano.
• 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.
• Product of P-polynomial association schemes. (abstract)
• On $s$-distance sets in real hyperbolic space.

Contact

• Email: ziqing@uga.edu
• Email: xiang@ziqing.org
• Office: Boyd 427K
• Mobile Phone: +86-137-6682-2808
• Mailing address:
  Department of Mathematics
  Boyd Graduate Studies Research Center
  University of Georgia
  Athens, GA, 30602, USA

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