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Qing XIANG

Qing XIANG

Chair Professor
someemail@sustech.edu.cn

Research Interests

Combinatorial Designs; Finite Geometry; Coding Theory; Additive Combinatorics

Professor Qing Xiang received his Ph.D. from The Ohio State University in 1995. In 1999, he was awarded the Kirkman Medal by the Institute of Combinatorics and its Applications (ICA) for his outstanding contributions to combinatorics. He previously served as the Bateman Instructor at the California Institute of Technology (Caltech), held a tenured faculty position at the University of Delaware, and was a Chair Professor at Zhejiang University. He is currently a Chair Professor at Southern University of Science and Technology (SUSTech).

Professor Xiang employs profound algebraic and number-theoretic tools to study problems in combinatorial designs, finite geometry, and coding theory, achieving a series of significant results. Together with his collaborators, he used Stickelberger’s theorem on Gauss sums in number theory to prove two conjectures proposed by Welch and Niho (1972) concerning the cross-correlation functions of m-sequences. The proof techniques have since found wide applications in other problems.

In his research on difference sets, he and Tao Feng constructed genuine skew Hadamard difference sets using higher-order cyclotomic classes. This was the first successful construction of difference sets using cyclotomic classes since Marshall Hall Jr.’s work in 1956, marking a groundbreaking achievement.

Additionally, in collaboration with David Chandler and Peter Sin, he applied the modular representation theory of classical groups and character sums to study error-correcting codes generated by certain combinatorial incidence matrices, computing their invariant factors and p-ranks. This work has been hailed as “truly elegant” by peers.

Publications：

  1. R. M. Wilson and Q. Xiang, Constructions of Hadamard difference sets, J. Combin. Theory (A) 77 (1997), 148--160.

  2. R. Evans, H. D. L. Hollmann, C. Krattenthaler, Q. Xiang, Gauss sums, Jacobi sums and p-ranks of cyclic difference sets, J. Combin. Theory (A) 87 (1999), 74--119.

  3. X. D. Hou, K. H. Leung, Q. Xiang, A generalization of an addition theorem of Kneser, J. Number Theory 97 (2002), 1--9.

  4. J. A. Davis and Q. Xiang, Negative Latin square type partial difference sets in nonelementary abelian 2-groups, J. London Math. Soc. 70 (2004), 125--141.

  5. M. Muzychuk and Q. Xiang, Symmetric Bush-type Hadamard matrices of order 4m^4 exist for all odd m, Proceedings AMS 134 (2006), 2197--2204.

  6. D. B. Chandler, P. Sin, Q. Xiang, The invariant factors of the incidence matrices of points and subspaces in PG(n,q) and AG(n,q), Trans. Amer. Math. Soc. 358 (2006), 4935--4957.

  7. D. B. Chandler, P. Sin, Q. Xiang, The permutation action of finite symplectic groups of odd characteristic on their standard modules, J. Algebra 318 (2007), 871--892.

  8. T. Feng, Q. Xiang, Cyclotomic constructions of skew Hadamard difference sets, J. Combin. Theory (A) 119 (2012), 245--256.

  9. T. Feng, Q. Xiang, Strongly regular graphs from unions of cyclotomic classes, J. Combin. Theory (B) 102 (2012), 982--995.

  10. J. Bamberg, M. Lee, K. Momihara, Q. Xiang, A new infinite family of hemisystems of the Hermitian surface, Combinatorica 38 (2018), 43--66.