Chuangxun Cheng's Home Page

Chuangxun Cheng
最斐悗
Department of Mathematics
Nanjing University

Nanjing University
22 Hankou Road
210093 Nanjing China
Office: Jiayi Building Yi-203 (樅眣瞼眣203)
E-Mail: cxcheng@nju.edu.cn

Teaching:

I teach Linear Algebra this semester.

Research:

My area of research is number thoery. I am also interested in algebraic geometry and representation theory. The following is a list of my publications and writings. PDF files may differ slightly from published versions.

The independence of Galois representations from Abelian varieties of GL2-type PDF
(With Junyun Chen and Yiding Cui) Preprint 2024
On the trace map of Lubin-Tate formal groups and a result of Lang-Tate PDF
(With Cheng Niu) Preprint 2024
Phase retrievable vectors and maximal spanning vectors PDF
(With Jiuyi Lu and Xiaoguang Shang) Preprint 2024
The phase retrievability of irreducible representations of finite groups PDF
Preprint 2024
Three MacWilliams type identities and quantum error-correcting G-codes PDF
(With Xiaoguang Shang) To appear in Adv. Math. Commun.
Remarks on frames from projective representations of locally compact groups PDF
(With Junyun Chen) J. Fourier Anal. Appl. 30 (2024), no. 5, Paper No. 49.
Some remarks on projective representations of compact groups and frames PDF
(With Guilin Li) Commun. Math. Stat. (2024 online).
Distinguishing newforms by the prime divisors of their Fourier coefficients PDF
(With Wei Wang) J. Number Theory 255 (2024), 148每165.
Orbit-injective covariant quantum channels PDF
(With Kai Liu and Deguang Han) Linear Algebra Appl. 668 (2023), 28每50.
On 羽-divisible O-modules over fields of characteristic p PDF
Asian J. Math. 27 (2023), no. 1, 1每56.
On the existence of maximal spanning vectors in L2(Q2) and L2(F2((T))) PDF
(With Jiuyi Lu) J. Number Theory 245 (2023), 187每202.
Phase retrieval for continuous Gabor frames on locally compact abelian groups PDF
(With Hailong Xu, Wen-Lung Lo) Banach J. Math. Anal. 15 (2021), no. 2, Paper No. 32, 22 pp.
On twisted group frames PDF
(With Deguang Han) Linear Algebra Appl. 569 (2019), 285-310.
Phase retrievable projective representation frames for finite abelian groups PDF
(With Joseph Bremman, Deguang Han, Ted Juste, and Lan Li) J Fourier Anal Appl (2019) 25, 86-100.
On multiplicities of Galois representations in cohomology groups of Shimura curves PDF
(With Fu Ji) Math. Res. Lett. (2018) Volume 25, Number 3, 759-782.
Breuil O-windows and 羽-divisible O-modules PDF
Trans. Amer. Math. Soc. 370 (2018), no. 1, 695-726.
O-displays and 羽-divisible formal O-modules PDF
(With Tobias Ahsendorf and Thomas Zink) Journal of Algebra 457 (2016) 129-193.
A character theory for projective representations of finite groups PDF
Linear Algebra and its Applications, Volume 469, 15 March 2015, 230-242.
Explicit examples for the Breuil-M谷zard conjecture PDF
Journal of Number Theory 157 (2015) 199-214.
Multiplicity one of regular Serre weights PDF
Israel Journal of Mathematics November 2013, Volume 198, Issue 1, 419-466.
Local Diophantine properties of Shimura curves and the Fp-gonality PDF
Funct. Approx. Comment. Math. Volume 49, Number 2 (2013), 321-330.
Mod p representations of SL2(Qp) PDF
Journal of Number Theory 133 (2013) 1312-1330.
Rank two Breuil modules: basic structures PDF
Journal of Number Theory 132 (2012) 2379-2396.
Some results on Galois representations attached to motives of GL2-type PDF
Funct. Approx. Comment. Math. Volume 49, Number 2 (2013), 371-381.
A relation between the Brauer group and the Tate-Shafarevich group PDF
Funct. Approx. Comment. Math. Volume 47, Number 2 (2012), 149-156.
Some consequences of Schanuel's Conjecture PDF
(With Arizona Winter School 2008 project group) Journal of Number Theory 129 (2009) 1464-1467.

Other Writings:

Patching and modularity PDF
Notes on patching via an explicit modularity theorem.
Modular forms and Fermat's Last Theorem PDF
Introduction to Wiles' proof on Fermat Last Theorem in Chinese.
Deformations of 羽-divisible O-modules via O-displays PDF
Long version of the part on deformations of the paper On 羽-divisible O-modules over fields of characteristic p.
A character theory for projective representations of finite groups PDF
Long version of the paper with the same title.
On the rings of projective characters of abelian groups and dihedral groups PDF
(With Fu Ji) Notes on projective representations of abelian groups and dihedral groups.
A short note on the Breuil-M谷zard conjecture PDF
(With Hendrik Verhoek) Lecture notes of two talks given by the authors at Workshop Around the Breuil-M谷zard Conjecture.
Mod p representations of local division algebras over p-adic fields PDF
Some computation on mod p representations of division algebras.

Teaching:

Research:

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