Research

I do research in algebraic geometry. From the titles of my publications, you can see clearly that the majority of my work studies rationally connected varieties, their geometry, topology, and arithmetic. For me, the subject itself is a real gem, true love of the heart. If you would like to get a rough idea of subject, I recommend two excellent surveys by the Master on low degree polynomials and the simplest algebraic varieties. Sometimes I talk to other people and work on different subjects as well.

Publication

Preprints

• (With János Kollár) Stable maps of curves and algebraic equivalence of 1-cycles, arXiv

• Local-global principle and integral Tate conjecture for certain varieties, arXiv.

• Zero cycles on rationally connected varieties over Laurent fields, arXiv.

• (with Jason Starr) All smooth low degree complete intersections are rationally simply connected, available upon request.

• (with Jason Starr) Separable rational connectedness and weak approximation in positive characteristic. arXiv

• Towards the symplectic Grabber-Harris-Starr theorems, arXiv.

• (with Lie Fu) Motivic hyperhahler resolution conjecture for Hilbert scheme of K3 surfaces, availabe on Lie's webpage.

Journal articles

Click on the title to read the articles.

1. (with Starr, Jason M. Zong, Runhong) Weak approximation for Fano complete intersections in positive characteristic. Ann. Inst. Fourier (Grenoble) 72 (2022), no. 4, 1503–1534.

2. (with Li, Zhiyuan) Moduli space of quasi-polarized K3 surfaces of degree 6 and 8. Chinese Ann. Math. Ser. B 42 (2021), no. 3, 427–450.

3. (with Zong, Runhong) Weak approximation for isotrivial families. J. Reine Angew. Math. 752 (2019), 1–23.
   

4. (with Fu, Lie) 2-cycles sur les hypersurfaces cubiques de dimension 5. (French) (2-cycles on the cubic hypersurfaces of dimension 5) Math. Z. 293 (2019), no. 1-2, 661–676.

5. (with Fu, Lie) Motivic multiplicative McKay correspondence for surfaces. Manuscripta Math. 158 (2019), no. 3-4, 295–316.

6. (with Fu, Lie and Vial, Charles) Motivic hyper-Kahler resolution conjecture, I: generalized Kummer varieties. Geom. Topol. 23 (2019), no. 1, 427–492.

7. (with Zhang, Letao) Weak approximation for cubic hypersurfaces and degree 4 del Pezzo surfaces. Int. Math. Res. Not. IMRN 2018, no. 3, 762–784.

8. Hasse principle for three classes of varieties over global function fields. Duke Math. J. 166 (2017), no. 17, 3349–3424.

9. (with Chen, Jungkai ; Jiang, Zhi) Irregular varieties with geometric genus one, theta divisors, and fake tori. Adv. Math. 320 (2017), 361–390

10. (with Xu, Chenyang) Finiteness of fundamental groups. Compos. Math. 153 (2017), no. 2, 257–273.

11. (with Li, Zhiyuan) Integral Hodge classes on fourfolds fibered by quadric bundles. Proc. Amer. Math. Soc. 144 (2016), no. 8, 3333–3345.

12. (with Greer, Francois and Li, Zhiyuan) Picard groups on moduli of K3 surfaces with Mukai models. Int. Math. Res. Not. IMRN 2015, no. 16, 7238–7257.

13. Weak approximation for cubic hypersurfaces. Duke Math. J. 164 (2015), no. 7, 1401–1435.

14. Separable rational connectedness and stability. Rational points, rational curves, and entire holomorphic curves on projective varieties, 155–159, Contemp. Math., 654, Centre Rech. Math. Proc., Amer. Math. Soc., Providence, RI, 2015.

15. R-equivalence on del Pezzo surfaces of degree 4 and cubic surfaces. Taiwanese J. Math. 19 (2015), no. 6, 1603–1612.

16. Symplectic geometry and rationally connected 4-folds. J. Reine Angew. Math. 698 (2015), 221–244.

17. (with Zong, Hong R.) One-cycles on rationally connected varieties. Compos. Math. 150 (2014), no. 3, 396–408.

18. Symplectic geometry of rationally connected threefolds. Duke Math. J. 161 (2012), no. 5, 803–843.