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Ziqing Xiang

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

Design Theory

• 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. to appear. 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.

Papers submitted

• Rational designs, joint work with Zhen Cui and Jiacheng Xia. (PDF)
• Support varieties for Hecke algebras, joint work with Dan Nakano. (PDF)

Preprint

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

Papers in preparation

• An explicit construction of spherical designs
• Hamiltonian thickness, joint work with Yaokun Wu and Yinfeng Zhu. (abstract)
• Classification problem of certain spherical embeddings of strongly regular graphs, joint work Eiichi Bannai, Etsuko Bannai, Wei-Hsuan Yu and Yan Zhu.
• 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)
• $s$-distance set in real hyperbolic space.

Contact

• Email: ziqing@uga.edu
• 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

• Association Schemes
• Designs
• Graphs
• Iwahori-Hecke Algebras
• Representation Theory
• Symbolic Dynamics
• Schur Algebras