• 职称(Positional titles):

  • 教授

  • 所在部门(Department):

  • 代数教研室

  • 研究方向(Research direction):

  • 代数与数论

  • 办公室(Office):

  • 教二楼 618

  • E-mail :

  • xufeiATmath.ac.cn

  • 个人主页(Personal home page):

个人简介 论文出版物 教学经历 科研项目及会议 获奖情况 Personal profile

姓名:徐飞, 男,首都师范大学数学科学学院教授,博士生导师。
研究方向: 算术代数几何

1、A remark on spinor norms of local integral rotations, I. Pacific J. Math. 136,(1989) 81-84.
2、Spinor norms of local integral rotations in characteristic 2,J. Number Theory 32, (1989) 289-296.
3、Spinor norms of global integral rotations (in Chinese),Northeastern Mathematical Journal 5, (1989) 293-300.
4、On Poincare series, Proceedings of the special program at Nankai Institute of Mathematics, Algebraic Geometry and Algebraic Number Theory, World Scientific (1992) 157-172.
5、Integral spinor norms in dyadic local fields I, Pacific J. Math. 157 (1993) 179-200.
6、Integral spinor norms in dyadic local fields II, Acta Arith. LXIII.3 (1993) 223-232.
7、Generation of integral orthogonal groups over dyadic local fields, Pacific J. Math. 167 (1995) 385-398.
8、A note on finitely generated torsion module over Zp[[T]], Algebra Colloq. 2 (1995) 351-354.
9、Kolyvagin's "Euler systems" in cyclotomic function fields, J. Number Theory. 57 (1996), 114-121. (joint with Keqin Feng)
10、Maximal independent systems of units in global function fields, Acta Arith. LXXVIII.1 (1996), 1-10. (joint with Jianqiang Zhao)
11、Riemann-Hurwitz formula in basic Zs-extensions, Acta Arith. LXXXI,1 (1997), 1-10. (joint with Ouyang Yi)
12、Representations of indefinite quadratic forms, J. reine und angew. Math. 494 (1998), 129-140. (joint with J.S.Hsia and Y.Y.Shao)
13、Arithmetic Springer theorem on quadratic forms under field extensions of odd degree, Contemp. Math. (AMS) 249 (1999), 175-197.
14、Representations of indefinite ternary quadratic forms over number fields, Math. Z. 234 (2000), 115-144.
15、Euler system in global function fields, Israel J. Math. 124 (2001), 367-379. (joint with Jianqiang Zhao)
16、Representation masses of spinor genera, Duke Math. J. 110 (2001) 279-307.
17、Minimal norm Jordan splittings of quadratic lattices over complete dyadic discrete valuation rings, Arch der Math. 81 (2003) 402-415.
18、On representations of spinor genera, Compositio Math. 140 (2004) 287-300. (joint with Wai Kiu Chan)
19、Representations by spinor genera of ternary quadratic forms, Contemp. Math. (AMS) 344 (2004), 323-337. (joint with R. Schulze-Pillot)
20、On representations of spinor genera II, Math. Ann. 332 (2005) 37-53.
21、Sums of three squares over imaginary quadratic fields, Forum Math.18 (2006), 585-601. (joint with Chungang Ji and Yuanhua Wang)
22、Spinor genera in characteristic 2, Memoirs of AMS Vol.194 (2008). (joint with Yuanhua Wang)
23、Universal quadratic forms over polynomial rings, J. Korean Math.Soc.45 (2008), no.5, 1311-1322. (joint with Myung-Hwan Kim and Yuanhua Wang)
24、Brauer-Manin obstruction for integral points of homogeneous spaces and reprensentation by integral quadratic forms, Compositio Math.145 (2009), 309-363. (joint with J.-L. Colliot-Thelene)
25、Tower of the maximal abelian extensions of local fields and its application, Manuscript Math. 129 (2009), 1-28. (joint with Dasheng Wei)
26、Realization of numbers as the degrees of maps between manifolds, Acta Mathematica Sinica 26 (2010), 1413-1424. (joint with Young Min Lee)
27、Integral spinor norms in dyadic local fields III, Science China Mathematics, 53 (2010), 2425-2446. (joint with Jianrui Lv)
28、Integral points for multi-norm tori, Proc. Lond. Math. Soc. 104 (2012), 1019-1044. (joint with Dasheng Wei)
29、Integral points for groups of multiplicative type, Adv. Math. 232 (2013), 36-56. (joint with Dasheng Wei)
30、Strong approximation for the total space of certain quadratic fibrations, Acta Arith. 157 (2013), 169-199. (joint with Colliot-Thelene)
31、Strong approximation for certain quadric fibrations with compact fibers, Adv. Math. 281 (2015), 279-295.
32、Very strong approximation for algebraic varieties, Math. Ann. 363 (2015), 701-731. (joint with Qing Liu)
33、Counting integral points in certain homogeneous spaces, J. Algebra 448 (2016), 350-398. (joint with Dasheng Wei)
34、Strong approximation with Brauer-Manin obstruction for toric varieties, Ann. Inst. Fourier, Grenoble 68 (2018), 1879-1908. (joint with Yang Cao)
35、Strong approximation with Brauer-Manin obstruction for groupic varieties, Proc. Lond. Math. Soc. 117 (2018), 727-750. (joint with Yang Cao)
36、Comparing descent obstruction and Brauer-Manin obstruction for open varieties, Trans. Amer. Math. Soc.371 (2019), 8625-8650. (joint with Yang Cao and Cyril Demarche)
37、Arithmetic purity of strong approximation for homogeneous spaces, J. Math. Pures Appl. 132 (2019), 334-368. (joint with Yang Cao and Yongqi Liang)
38、Brauer-Manin obstruction for Markoff surfaces, Ann. Sc. Norm. Super. Pisa Cl. Sci. XXI (2020), 1257–1313. (joint with Colliot-Thelene and Dasheng Wei)
39、On indefinite and potentially universal quadratic forms over number fields, Trans. Amer. Math. Soc. 375 (2022) 2459-2480. (joint with Yang Zhang)

1. 89年10月-90年12月:南开数学所博士后。
2. 91年1月-92年12月:中国科技大学博士后。
3. 93年1月-2000年5月:中国科技大学副教授。
5. 2008年1月-至今:首都师范大学教授。

3. 2004年-2007年:国家自然科学基金杰出青年基金,代数数论。
4. 2015年-2018年:国家自然科学基金面上项目,代数簇上整点和有理点的上同调方法。
5. 2017年-2021年:国家自然科学基金重点项目:数域上代数簇的周群,K-群及其不变量研究。


Name: Fei XU
Research area: Arithmetic Geometry

Teaching experience:
1. Oct.1989-Nov.1990, a post-doctoral researcher at Nankai Institute of Mathematics.
2. Dec.1990-Dec.1992, a post-doctoral researcher at University of Science and Technology of China.
3. Jan.1993-Aug.1999, an associate professor at University of Science and Technology of China.
4. Sep.1999-Dec.2007, professor at Academy of Mathematics and System Sciences, Chinese Academy of Sciences
5. Jan.2008-now, professor at Capital Normal University.

1. 1996-1998: Fellowship of Alexander von Humboldt Foundation.
2. 2000-2003: Hundred Talent Program of Chinese Academy of Sciences
3. 2004-2007: Outstanding youth grant for National Natural Science Foundation of China.

The first prize of natural sciences of Chinese Ministry of Education, 2019.