I am interested in algebraic number theory, especially in the theory of Drinfeld modules and related topics.

My research is supported in part by the Simons Foundation.

Research Papers

1. Drinfeld discriminant function and Fourier expansion of harmonic cochains (with Fu-Tsun Wei), Mathematische Annalen 388 (2024), 1379–1435.

2. Isomorphism classes of Drinfeld modules over finite fields (with Valentijn Karemaker and Jeffrey Katen), Journal of Algebra 644 (2024), 381-410.

3. The growth of the discriminant of the endomorphism ring of the reduction of a rank 2 generic Drinfeld module (with Alina Cojocaru), Journal of Number Theory 237 (2022), 15-39.

4. Computing endomorphism rings and Frobenius matrices of Drinfeld modules (with Sumita Garai), Journal of Number Theory 237 (2022), 145-164.

5. Endomorphism rings of reductions of Drinfeld modules (with Sumita Garai), Journal of Number Theory (special issue in memory of David Goss) 232 (2022), 155–176.

6. Galois extensions and a conjecture of Ogg (with Krzysztof Klosin), Proceedings of the American Mathematical Society 148 (2020), 3821-3834.

7. On Ribet's isogeny for J0(65) (with Krzysztof Klosin), Proceedings of the American Mathematical Society 146 (2018), 3307-3320.

8. Drinfeld-Stuhler modules, Research in the Mathematical Sciences 5 (2018), Paper No. 40, 1-33.

9. The rational torsion subgroups of Drinfeld modular Jacobians and Eisenstein pseudo-harmonic cochains (with Fu-Tsun Wei), Mathematische Zeitschrift 287 (2017), 521-546.

10. Optimal quotients of Jacobians with toric reduction and component groups (with Joseph Rabinoff), Canadian Journal of Mathematics 68 (2016), 1362-1381.

11. Graph Laplacians, component groups and Drinfeld modular curves, Münster Journal of Mathematics 9 (2016), 221-251.

12. On Garland's vanishing theorem for SL(n), European Journal of Mathematics 2 (2016), 579-613.

13. On component groups of Jacobians of quaternionic modular curves, Archiv der Mathematik (special issue in honor of Ernst-Ulrich Gekeler) 107 (2016), 315-328.

14. On the Eisenstein ideal over function fields (with Fu-Tsun Wei), Journal of Number Theory (special issue in honor of Winnie Li) 161 (2016), 384-434.

15. Drinfeld modules, Frobenius endomorphisms, and CM-liftings (with Alina Cojocaru), International Mathematics Research Notices 17 (2015), 7787-7825.

16. The Eisenstein ideal and Jacquet-Langlands isogeny over function fields (with Fu-Tsun Wei), Documenta Mathematica 20 (2015), 551-629.

17. Non-archimedean uniformization and monodromy pairing, Contemporary Mathematics 605 (2013), 123-160.

18. D-elliptic sheaves and odd Jacobians, Journal of Number Theory (special issue in memory of of David Hayes) 133 (2013), 1012-1026.

19. Local diophantine properties of modular curves of D-elliptic sheaves, Journal für die reine und angewandte Mathematik 664 (2012), 115-140.

20. On generators of arithmetic groups over function fields, International Journal of Number Theory 7 (2011), 1573-1587.

21. On Jacquet-Langlands isogeny over function fields, Journal of Number Theory 131 (2011), 1149-1175.

22. On finite arithmetic simplicial complexes, Proceedings of the American Mathematical Society 139 (2011), 111-124.

23. Endomorphisms of exceptional D-elliptic sheaves, Mathematische Zeitschrift 266 (2010), 407-423.

24. On hyperelliptic modular curves over function fields, Archiv der Mathematik 92 (2009), 291-302.

25. Genus formula for modular curves of D-elliptic sheaves, Archiv der Mathematik 92 (2009), 237-250.

26. Modular varieties of D-elliptic sheaves and the Weil-Deligne bound, Journal für die reine und angewandte Mathematik 626 (2009), 115-134.

27. On eigenvalues of p-adic curvature, Manuscripta Mathematica 127 (2008), 397-410.

28. Modular curves of D-elliptic sheaves are asymptotically optimal, Mathematical Research Letters 15 (2008), 525-536.

29. Analogue of the degree conjecture over function fields, Transactions of the American Mathematical Society 359 (2007), 3483-3503.

30. Abelian subvarieties of Drinfeld Jacobians and congruences modulo the characteristic, Mathematische Annalen 337 (2007), 139-157.

31. The number of rational points on Drinfeld modular varieties over finite fields, International Mathematics Research Notices Article ID 94356 (2006), 1-36.

32. On the torsion of optimal elliptic curves over function fields, Mathematical Research Letters 13 (2006), 321-331.

33. On the variation of Tate-Shafarevich groups of elliptic curves over hyperelliptic curves, Journal of Number Theory 115 (2005), 249-283.

34. Rigid-analytic geometry and abelian varieties, Contemporary Mathematics 388 (2005), 145-160.

35. Pesenti-Szpiro inequality for optimal elliptic curves, Journal of Number Theory 114 (2005), 361-393.

36. On component groups of Jacobians of Drinfeld modular curves, Annales de l'Institut Fourier 54 (2004), 2163-2199.

37. On the degree of modular parametrizations over function fields, Journal of Number Theory 97 (2002), 317-349.

38. On coset coverings of solutions of homogeneous cubic equations over finite fields (with Ara Alexanian), Electronic Journal of Combinatorics 8 (2001), #R22.

Preprints

1. Ogg's conjectures over function fields (with Cécile Armana and Sheng-Yang Kevin Ho). 

2. D-elliptic sheaves and the Hasse principle (with Keisuke Arai, Shin Hattori, and Satoshi Kondo).

3. On Drinfeld modular curves for SL(2) (with Jesse Franklin and Sheng-Yang Kevin Ho).

4. On ideal class numbers of totally degenerate number rings (with Ruben Hambardzumyan). 

Expository Notes (not intended for publication)

1. An overview of the theory of Drinfeld modules (2017).

2. Honda-Tate theorem for elliptic curves (2012).

3. Mass formula for central division algebras over function fields (2004).

4. Notes on "Heights and the special values of L-series" by B. Gross (2004).

5. Notes on "Kolyvagin's work on modular elliptic curves" by B. Gross (2001).

6. Heegner point computations over function fields (2001).