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73882必赢网页版月：2022年73882必赢网页版1月---2025年73882必赢网页版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73882必赢网页版月：2021年73882必赢网页版1月---2023年73882必赢网页版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73882必赢网页版科学基金项目，项目批准号 11801260，

26 万元， 起止年73882必赢网页版月：2019年73882必赢网页版1月---2021年73882必赢网页版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73882必赢网页版月：2019年73882必赢网页版1月---2022年73882必赢网页版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