Research Interests
My research domain is arithmetic geometry. Research topics I'm particularly interested in include rational points of homogeneous varieties, arithmetic of quadratic forms and related structures, Galois cohomology of linear algebraic groups, etc.
Grants
1. 主持 （PI）：
Universal quadratic forms and Hilbert's seventeenth problem over semi-global fields
泛表示的二次型和半整体域上的 Hilbert 第十七问题
National Natural Science Foundation of China, Regular Program No. 12171223,
510,000 RMB yuan, Jan. 2022---Dec. 2025;
国家自然科学基金，面上项目，项目批准号 12171223，
51 万元， 起止年月：2022年1月---2025年12月;
2. 主持 （PI）：
Chow groups and unramified cohomology of quadrics in characteristic 2
特征为 2 时二次超曲面的周群和非分歧上同调
Guangdong Basic and Applied Basic Research Foundation, Program No. 2021A1515010396
RMB 100 000 yuan, Jan. 2021---Dec. 2023.
广东省基础与应用基础研究基金，面上项目，项目编号 2021A1515010396
10 万元， 起止年月：2021年1月---2023年12月.
3. 主持 （PI）：
Division algebras and arithmetic of quadratic forms over semi-global fields
半整体域上的可除代数和二次型相关算术问题
National Natural Science Foundation of China, Youth Program No. 11801260,
260,000 RMB yuan, Jan. 2019---Dec. 2021;
国家自然科学基金，青年科学基金项目，项目批准号 11801260，
26 万元， 起止年月：2019年1月---2021年12月;
4. 参与 (Participate)：
Higher rank Kuznetsov formulas and applications
高秩 Kuznetsov 公式及其应用
National Natural Science Foundation of China, Program No. 11871261,
550,000 RMB yuan, Jan. 2019---Dec. 2022;
国家自然科学基金，面上项目，项目批准号 11871267，
55 万元， 起止年月：2019年1月---2022年12月;
Preprints
1. (with Ahmed Laghribi and Peng Sun) Chow Groups of Quadrics in Characteristic Two, preprint available at arXiv:2101.03001
2. (with Zilong He) Pythagoras number of quartic orders containing $\sqrt{2}$, preprint available at arXiv:2204.10468
Publications
1. (with Sunghan BAE and Linsheng YIN) Artin L-functions and modular forms associated to quasi-cyclotomic fields, Acta Arithmetic, 143 (2010), 59--80
2. Weak approximation over function fields of curves over large or finite fields, Math. Ann. 348 (2010) No. 2, 357–377.
3. Local-global principle for quadratic forms over fraction fields of two-dimensional henselian domains, Annales de l’Institut Fourier, 62 (2012) No. 6, 2131–2143.
4. Division algebras and quadratic forms over fraction fields of two-dimensional henselian domains, Algebra & Number Theory, 7 (2013) No. 8, 1919–1952.
5. Hasse principle for simply connected groups over function fields of surfaces, Journal of Ramanujan Mathematical Society, 29 (2014) No. 2, 155–199.
6. The Pythagoras number and the $u$-invariant of Laurent series fields in several variables, Journal of Algebra, 426 (2015), 243–258.
7. A cohomological Hasse principle over two-dimensional local rings, International Mathematics Research Notices, 14 (2017), 4369–4397.
8. Reduced norms of division algebras over complete discrete valuation fields of local-global type, Journal of Algebra and Its Applications, (2020) 2050217, 16pp
9. (with Zhengyao Wu) On the Rost divisibility of henselian discrete
valuation fields of cohomological dimension 3, Annals of K-theory, 5 (2020) No. 4, 677-707
10. (with Peng Sun) Unramified Cohomology of Quadrics in Characteristic Two, Manuscripta Mathematica, 171 (2023) No. 1-2, 263–294 .
11. (with Zilong He) On k-universal quadratic lattices over unramified dyadic local fields, Journal of Pure and Applied Algebra, 227 (2023) No.7, 107344, 32pp.
12. (with Zilong He and Fei Xu) On indefinite k-universal integral quadratic forms over number fields, Mathematische Zeitschrift, 304 (2023) , Article number 20, 26pp.
13. (with Zilong He) On $n$-universal quadratic forms over dyadic local fields, to appear in Science China. Mathematics, preprint available at arXiv:2204.01997
Preprints
1. (with Ahmed Laghribi and Peng Sun) Chow Groups of Quadrics in Characteristic Two, preprint available at arXiv:2101.03001
2. (with Zilong He) Pythagoras number of quartic orders containing $\sqrt{2}$, preprint available at arXiv:2204.10468
Publications
1. (with Sunghan BAE and Linsheng YIN) Artin L-functions and modular forms associated to quasi-cyclotomic fields, Acta Arithmetic, 143 (2010), 59--80
2. Weak approximation over function fields of curves over large or finite fields, Math. Ann. 348 (2010) No. 2, 357–377.
3. Local-global principle for quadratic forms over fraction fields of two-dimensional henselian domains, Annales de l’Institut Fourier, 62 (2012) No. 6, 2131–2143.
4. Division algebras and quadratic forms over fraction fields of two-dimensional henselian domains, Algebra & Number Theory, 7 (2013) No. 8, 1919–1952.
5. Hasse principle for simply connected groups over function fields of surfaces, Journal of Ramanujan Mathematical Society, 29 (2014) No. 2, 155–199.
6. The Pythagoras number and the $u$-invariant of Laurent series fields in several variables, Journal of Algebra, 426 (2015), 243–258.
7. A cohomological Hasse principle over two-dimensional local rings, International Mathematics Research Notices, 14 (2017), 4369–4397.
8. Reduced norms of division algebras over complete discrete valuation fields of local-global type, Journal of Algebra and Its Applications, (2020) 2050217, 16pp
9. (with Zhengyao Wu) On the Rost divisibility of henselian discrete
valuation fields of cohomological dimension 3, Annals of K-theory, 5 (2020) No. 4, 677-707
10. (with Peng Sun) Unramified Cohomology of Quadrics in Characteristic Two, Manuscripta Mathematica, 171 (2023) No. 1-2, 263–294 .
11. (with Zilong He) On k-universal quadratic lattices over unramified dyadic local fields, Journal of Pure and Applied Algebra, 227 (2023) No.7, 107344, 32pp.
12. (with Zilong He and Fei Xu) On indefinite k-universal integral quadratic forms over number fields, Mathematische Zeitschrift, 304 (2023) , Article number 20, 26pp.
13. (with Zilong He) On $n$-universal quadratic forms over dyadic local fields, to appear in Science China. Mathematics, preprint available at arXiv:2204.01997
