向青
职称:讲席教授
邮箱:xiangq@sustech.edu.cn
研究方向:Combinatorics, Finite Geometry, Algebraic Coding Theory
个人简介
向青, 讲席教授。研究领域包括组合设计、有限几何、编码理论和加法组合。1995年毕业于俄亥俄州立大学,获博士学位。1999年获得国际组合数学及其应用协会颁发的Kirkman奖章。曾任美国加州理工学院Bateman Instructor, 美国特拉华(Delaware)大学终身教职,和浙江大学讲座教授。现为南方科技大学讲席教授。
向青教授用深刻的代数和数论工具来研究组合设计,有限几何,和编码理论中的问题,取得了一系列的重要成果。他与合作者用数论中深刻的关于高斯和的Stickelberger定理证明了m-序列交错相关函数中由Welch和Niho在1972年提出的两个猜想, 其证明方法在其它问题上有一系列的应用。在差集的研究中,与冯涛一起利用高阶分圆类构造出真正的斜Hadamard差集;这是在Marshall Hall Jr.1956年的工作后第一次成功地用分圆类构造出差集,具有突破性意义。他与David Chandler和Peter Sin一起用典型群的模表示理论与特征和来研究一些组合关联矩阵所生成的纠错码,并计算其不变因子和p-秩, 这被认为是“的确非常优美”的工作。
研究领域
组合数学,有限几何,代数编码
代表论文
1. 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.
2. H. D. L. Hollmann, Q. Xiang, A proof of the Welch and Niho conjectures on cross-correlations of binary m-sequences, Finite Fields Appl. 7 (2001), 253–286.
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. 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.
5. 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.
6. 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.
7. T. Feng, Q. Xiang, Cyclotomic constructions of skew Hadamard difference sets, J. Combin. Theory (A) 119 (2012), 245–256.
8. T. Feng, Q. Xiang, Strongly regular graphs from unions of cyclotomic classes, J. Combin. Theory (B) 102 (2012), 982–995.
9. J. Bamberg, M. Lee, K. Momihara, Q. Xiang, A new infinite family of hemisystems of the Hermitian surface, Combinatorica 38 (2018), 43–66.
10. P. Sin, J. Sorci, Q. Xiang, Linear representations of finite geometries and associated LDPC codes, J. Combin. Theory (A) 173 (2020), Paper No. 105238, 15pp.
11. B. Schmidt, D. Q. Wong, Q. Xiang, Constructions of Butson Hadamard matrices invariant under Abelian p-groups, J. Combin. Theory (A) 181 (2021), Paper No. 105433, 23pp.
12. T. Feng, K. Momihara, M. Rodgers, Q. Xiang, H. Zou, Cameron-Liebler line classes with parameter x=(q+1)^2/3, Adv. Math. 385 (2021), Paper No. 107780, 31 pp.