Research

Here are some of my research papers: 

1. A characteristic p analogue of the André--Pink--Zannier conjecture.
   With J. Lam, submitted.

2. Reductions of abelian varieties and K3 surfaces.
   With Y. Tang, JNT Biennial conference proceedings.

3. Integral canonical models of exceptional Shimura varieties.
   With B. Bakker and J. Tsimerman, submitted.

4. A p-adic analogue of Borel's theorem.
   With A. Oswal and X. Zhu, and an appendix by A. Patel, submitted.

5. Just-likely intersections on Hilbert modular surfaces.
   With Asvin G. and Q. He, Mathematische Annalen.  

6. Canonical Heights on Shimura Varieties and the André-Oort Conjecture
   With J.  Pila and J. Tsimerman, and an appendix by H. Esnault and M. Groechenig, submitted. 

7. The existence of abelian varieties not isogenous to Jacobians over global fields.
   With J. Tsimerman, Duke Mathematical Journal.

8. Finiteness of reductions of Hecke orbits.
   With M. Kisin, J. Lam and P. Srinivasan, Journal of the European Mathematical Society.
   My talk on this work.

9. Picard Ranks of K3 surfaces and the Hecke orbit conjecture.
   With D. Maulik and Y. Tang, Inventiones.

10. Exceptional jumps of Picard ranks of reductions of K3 surfaces over number fields.
    With Arul Shankar, Y. Tang and S. Tayou, Forum of Mathematics, Pi.

11. The rank two p-curvature conjecture on generic curves.
    With A. Patel and J.P. Whang, Advances in Mathematics.

12. Counting elliptic curves by conductor.
    With Arul Shankar and X.Wang, Compositio.

13. Reductions of abelian surfaces over global function fields.
    With D. Maulik and Y. Tang, Compositio.

14. Almost ordinary abelian varieties over finite fields.
    With A. Oswal, Journal of the London Mathematical Society.

15. Exceptional splitting of reductions of abelian surfaces.
    With Y. Tang, Duke Mathematical Journal.

16. Serre-Tate theory for Shimura variaties of Hodge type.
    With R. Zhou, Math Zeitschrift.
    My talk on this work.

17. Unlikely intersections in finite characteristic.
    With J. Tsimerman, Forum of Mathematics, Sigma.

18. The p-curvature conjecture and monodromy around simple closed loops.
    Duke Mathematical Journal.
    My talk on this work.

19. The Hecke orbit conjecture for "modèles étranges".
    Preprint.

20. 2-Selmer groups of hyperelliptic curves with marked points.
    Transactions of the AMS.