欧阳毅  (教授)

My research interest is Number Theory and Arithmetic Geometry, and their applications to cryptography and coding theory. Currently I am interested in the following subjects:

(1) Fontaine theory of p-adic representations and (φ,Γ)-modules, and its connection to Iwasawa theory.

(2) Theory of elliptic curves and its application in cryptography.

(3) Class groups and class numbers of number fields and function fields, Cohen-Lenstra Heuristics.

注意： 近日有多名学生咨询研究生导师的事情，鉴于研究生导师肩负的巨大责任，特此声明：本人不接收没有深入了解的同学作为研究生，特别地对于科大本科生，本人原则上只接收指导过大研计划和/或毕业设计的同学。（当然，如果你没有看到这句话，说明你对于了解我其实并没有兴趣，那就相忘于江湖吧）

1.  Yi Ouyang and Jianfeng Xie, The growth of Tate-Shafarevich groups in cyclic extensions, Compositio Math. 158 (2022), 2014–2032.
   

2. Yi Ouyang, Sen Wang and Xianhong Xie, Almost balanced and uncorrelated quaternary sequence pairs of even length. JUSTC, 2022, 52(3): 4.

3. Xianhong Xie, Yi Ouyang, Honggang Hu and Ming Mao, Construction of three classes of Strictly Optimal Frequency-Hopping Sequence Sets, , Advances in Mathematics of Communications 2022.  doi: 10.3934/amc.2022024

4. Jianing Li， Yi Ouyang, Yue Xu, On abelian 2-ramification torsion modules of quadratic fields, Sci. China Math., 2022, doi: 10.1007/s11425-021-1946-0.

5. Bei Wang, Songsong Li, Yi Ouyang and Honggang Hu. Ready-Made Short Basis for GLV+GLS on High Degree Twisted Curves, AIMS Mathematics, 2022, 7(1): 306-314. doi: 10.3934/math.2022021.

6. Bei Wang, Xianhong Xie, Songsong Li, Yi Ouyang and Honggang Hu, General 4-GLV Lattice Reduction Algorithms, Proceedings of 2021 17th International Conference on Computational Intelligence and Security (CIS’2021), 430-434, 2021.

7. Jianing Li, Yi Ouyang, Yue Xu, 阿贝尔p 分歧扭子群和新Cohen-Lenstra 猜想, (Abelian p-ramification groups and new Cohen-Lenstra heuristics), Sci Sin Math. 51(2021), No. 10, 1635-1654.

8.  Bei Wang, Yi Ouyang， Songsong Li  and Honggang Hu: A New Twofold Cornacchia-Type Algorithm and Its Applications, Advances in Mathematics of Communications 2021, doi:10.3934/amc.2021026.

9. Jianing Li, Yi Ouyang, Yue Xu and Shenxing Zhang, l-Class groups of fields in Kummer towers, Publ. Mat. 66 (2022), 235–267.

10. Songsong Li, Yi Ouyang and Zheng Xu, Endomorphism rings of supersingular elliptic curves over F_p,，Finite Fields Appl. 62(2020), February 2020, 101619.

11. Songsong Li, Yi Ouyang and Zheng Xu, Neighborhood of the supersingular elliptic curve isogeny graph at j=0 and 1728, Finite Fields Appl. 61(2020), January 2020, 101600.

12. Yi Ouyang and Zheng Xu, Loops of isogeny graphs of supersingular elliptic curves at j=0, Finite Fields Appl. 58 (2019), 174-176. (local)

13. Yi Ouyang and Xianhong Xie, Linear complexity of generalized cyclotomic sequences of period 2p^m, Des. Codes Cryptogr. 87 (2019), no. 11, 2585-2596. (local)

14. Yang Liu and Yi Ouyang, On binary quadratic forms modulo n, Commun. Math. Stat. 7 (2019), no. 1, 61-67. (local)

15. Songsong Li and Yi Ouyang, Counting the solutions of λ₁x₁^k`+… λ_t x_t^kt≡ c mod n, J. Number Theory 187(2018), 41-65. (local)

16. Bei Wang, Yi Ouyang and Honggang Hu, Efficient Pairing Computation on Twisted Weierstrass Curves, Chinese J. Electronics 27(2018), 739-745.(local)

17. Yi Ouyang and Jinbang Yang, On a conjecture of Wan about limiting Newton polygons, Finite Fields Appl. 41(2016), 64-71. (local)

18. Yi Ouyang and Shenxing Zhang, Newton polygons of L-functions of polynomials x^d+ax^d-1^with p≡-1 mod d, Finite Fields Appl. 37(2016), 285-294. (local)

19. Yi Ouyang and Shenxing Zhang, Birch's lemma over global function fields, Proc. Amer. Math. Soc. 145(2017), 577-584.

20. Yi Ouyang and Jinbang Yang, Newton Polygons of L functions of polynomials x^d+ax, J. Number Theory 160(2016), 478-491.

21. Yi Ouyang and Shenxing Zhang, On second 2-descent and non-congruent numbers, Acta Arith. 170 (2015), 343-360. Errata, Acta Arith. 202 (2022), 203-203.

22. Yi Ouyang and Zhe Zhang, Hilbert genus fields of real biquadratic fields, Ramanujan J. 37(2015) 345-363.

23. Yi Ouyang and Zhe Zhang, Hilbert genus fields of biquadratic fields, Sci. China Math. 57, No. 10(2014), 2111--2122.

24. Yi Ouyang and Jinbang Yang, On the cohomology of semi-stable p-adic Galois representations, C. R. Math. Acad. Sci. Paris Vol. 352(2014), 557--561.

25. Yi Ouyang and Shenxing Zhang, On non-congruent numbers with 1 modulo 4 prime factors, Sci. China Math. 57, No. 3(2014), 649--658.

26. Yi Ouyang, Lectures on p-adic zeta functions and (φ,Γ)-modules, in Number Theory and Related Area, pp. 85-147, 2013.

27. Yi Ouyang, F. Xu, C. Xing and P. Zhang, Number Theory and Related Area, editor, Advanced Lecture in Mathematics, Vol.27, Higher Education Press and International Press, 2013.

28. Yiwen Ding and Yi Ouyang, A simple proof of Dieudonné-Manin classification Theorem, Acta. Math. Sin. (Engl. Ser.)  Vol. 28, No. 8 (2012), 1553--1558.

29. Yi Ouyang and Hang Xue, Class numbers of Cyclic 2-extensions and Gross conjecture over Q, Sci. China Math. Vol. 53, No. 9 (2010), 2447--2462.

30. Kumar Murty and Yi Ouyang, The growth of Selmer ranks of an abelian variety with complex multiplication, Pure and Appl. Math. Quarterly 2, No. 2(2006), 539-555.

31. Yi Ouyang, The Gross conjecture over rational function fields, Science in China, Ser. A. Mathematics 48, No. 12 (2005), 1609-1617.

32. Yi Ouyang, The universal Kolyvagin recursion implies Kolyvagin recursion, Acta. Math. Sinica, English Ser. 23, No.7 (2007), 1163-1172.

33. Yi Ouyang,On the universal norm distribution, J. Ramanujan Math. Soc. 17, No. 4 (2002), 287--311.

34. Greg W. Anderson and Yi Ouyang, A note on the cyclotomic Euler systems and the double complex method, Can. J. Math. 55, No.4(2003), 673--692

35. Yi Ouyang, The universal norm distribution and Sinnott's index formula, PAMS 130(2002), No. 8, 2203-2213.

36. Yi Ouyang, The group cohomology of universal ordinary distribution, Crelle 537(2001), 1--32.

37. My thesis Group cohomology of the universal ordinary distribution and its applications, University of Minnesota, advisor: Greg William Anderson. 2000.

38. Yi Ouyang and Fei Xu, Riemann-Hurwitz formula in Basic Zs-extensions, Acta Arith.LXXXI.1 (1997), 1--10.

1.  Jean-Marc Fontaine and Yi Ouyang, Theory of p-adic Galois representations, new version, 2022.

2.  Xianhong Xie, Yi Ouyang and Ming Mao, Vectorial bent functions and Linear Codes from Quadratic Forms, preprint, 2020.

3.  Jianing Li, Songsong Li and Yi Ouyang, Factorization of Hilbert class polynomials over prime fields, preprint, 2021. arXiv:2108.00168

4.  Yi Ouyang and Jianfeng Xie,Unboundedness of Tate-Shafarevich groups in fixed cyclic extensions, preprint, 2022.

5.  Xianhong Xie and Yi Ouyang, On vectorial functions with maximal number of bent components, preprint, 2022. 

6. Sen Wang, Yi Ouyang and Xianhong Xie, New Classes of Optimal and Distance Optimal Two or Three-weight Codes, preprint, 2022.

1.  Galois和Kummer对于代数数论发展的贡献, 厦门大学东南数学中心短期课程，2020年8月，中文版，英文版

2.  The China Legacy of Jean-Marc Fontaine, la Gazette des Mathématiciens No. 162，Octobre 2019, 15-17.

3.  (冯克勤, 欧阳毅) 中法数论代数几何合作, 《清华数学90年》，清华大学, 2017.

4.  仿佛来自虚空---亚历山大·格洛腾迪克的生平故事, 译自 Allyn Jackson的著名文章Comme Appelé du Néant, As If Summoned from the Void: The Life of Alexandre Grothendieck, Part I, Notices AMS, Vol 51, No. 9; Part II, Notices AMS, Vol 51, No. 10, 发表于《数学译林》.

5.  黎曼假设有关的数学巨匠和数学进展. 见《代数学III：代数学进阶》数字课程网站 (http://abook.hep.com.cn/1251847).

6.  艾米·诺特小传.  同上.

7.  二次曲线和p进数.   同上.

8.  Inverse limits and Galois Theory. 同上.

9.  Introduction to Iwasawa theory.

10.(葛力明, 欧阳毅, 田野, 邢朝平, 徐飞) 冯克勤先生简介, SCIENTIA SINICA Mathematica, 2021.