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

Curriculum Vitae


Publications
  1. Drinfeld-Stuhler modules , Research in the Mathematical Sciences, 5 (2018), Paper No. 40, 1-33.
  2. On Ribet's isogeny for J0(65) (with Krzysztof Klosin), Proceedings of the American Mathematical Society, 146 (2018), 3307-3320.
  3. The rational torsion subgroups of Drinfeld modular Jacobians and Eisenstein pseudo-harmonic cochains (with Fu-Tsun Wei), Mathematische Zeitschrift 287 (2017), 521-546.
  4. Optimal quotients of Jacobians with toric reduction and component groups (with Joseph Rabinoff), Canadian Journal of Mathematics 68 (2016), 1362-1381.
  5. Graph Laplacians, component groups and Drinfeld modular curves, Münster Journal of Mathematics 9 (2016), 221-251.
  6. On Garland's vanishing theorem for SL(n), European Journal of Mathematics 2 (2016), 579-613.
  7. On component groups of Jacobians of quaternionic modular curves, Archiv der Mathematik (Special issue in honor of Ernst-Ulrich Gekeler) 107 (2016), 315-328.
  8. 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.
  9. Drinfeld modules, Frobenius endomorphisms, and CM-liftings (with Alina Cojocaru), International Mathematics Research Notices 17 (2015), 7787-7825.
  10. The Eisenstein ideal and Jacquet-Langlands isogeny over function fields (with Fu-Tsun Wei), Documenta Mathematica 20 (2015), 551-629.
  11. Non-archimedean uniformization and monodromy pairing, Contemporary Mathematics 605 (2013), 123-160.
  12. D-elliptic sheaves and odd Jacobians, Journal of Number Theory (Special issue in honor of David Hayes) 133 (2013), 1012-1026.
  13. Local diophantine properties of modular curves of D-elliptic sheaves, Journal für die reine und angewandte Mathematik 664 (2012), 115-140.
  14. On generators of arithmetic groups over function fields, International Journal of Number Theory 7 (2011), 1573-1587.
  15. On Jacquet-Langlands isogeny over function fields, Journal of Number Theory 131 (2011), 1149-1175.
  16. On finite arithmetic simplicial complexes, Proceedings of the American Mathematical Society 139 (2011), 111-124.
  17. Endomorphisms of exceptional D-elliptic sheaves, Mathematische Zeitschrift 266 (2010), 407-423.
  18. On hyperelliptic modular curves over function fields, Archiv der Mathematik 92 (2009), 291-302.
  19. Genus formula for modular curves of D-elliptic sheaves, Archiv der Mathematik 92 (2009), 237-250.
  20. Modular varieties of D-elliptic sheaves and the Weil-Deligne bound, Journal für die reine und angewandte Mathematik 626 (2009), 115-134.
  21. On eigenvalues of p-adic curvature, Manuscripta Mathematica 127 (2008), 397-410.
  22. Modular curves of D-elliptic sheaves are asymptotically optimal, Mathematical Research Letters 15 (2008), 525-536.
  23. Analogue of the degree conjecture over function fields, Transactions of the American Mathematical Society 359 (2007), 3483-3503.
  24. Abelian subvarieties of Drinfeld Jacobians and congruences modulo the characteristic, Mathematische Annalen 337 (2007), 139-157.
  25. The number of rational points on Drinfeld modular varieties over finite fields, International Mathematics Research Notices Article ID 94356 (2006), 1-36.
  26. On the torsion of optimal elliptic curves over function fields, Mathematical Research Letters 13 (2006), 321-331.
  27. On the variation of Tate-Shafarevich groups of elliptic curves over hyperelliptic curves, Journal of Number Theory 115 (2005), 249-283.
  28. Rigid-analytic geometry and abelian varieties, Contemporary Mathematics 388 (2005), 145-160.
  29. Pesenti-Szpiro inequality for optimal elliptic curves, Journal of Number Theory 114 (2005), 361-393.
  30. On component groups of Jacobians of Drinfeld modular curves, Annales de l'Institut Fourier 54 (2004), 2163-2199.
  31. On the degree of modular parametrizations over function fields, Journal of Number Theory 97 (2002), 317-349.
  32. On coset coverings of solutions of homogeneous cubic equations over finite fields (with Ara Alexanian), Electronic Journal of Combinatorics 8 (2001), #R22.

Preprints
  1. Endomorphism rings of reductions of Drinfeld modules (with Sumita Garai)

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).