I am interested in algebraic number theory, especially in the theory of Drinfeld modular varieties and related topics.
My research is supported in part by the Simons Foundation.

Curriculum Vitae
Publications
  1. D-elliptic sheaves and odd Jacobians, Journal of Number Theory (Special Issue in honor of David Hayes) 133 (2013), 1012-1026.
  2. Local diophantine properties of modular curves of D-elliptic sheaves, Journal für die reine und angewandte Mathematik 664 (2012), 115-140.
  3. On generators of arithmetic groups over function fields, International Journal of Number Theory 7 (2011), 1573-1587.
  4. On Jacquet-Langlands isogeny over function fields, Journal of Number Theory 131 (2011), 1149-1175.
  5. On finite arithmetic simplicial complexes, Proceedings of the American Mathematical Society 139 (2011), 111-124.
  6. Endomorphisms of exceptional D-elliptic sheaves, Mathematische Zeitschrift 266 (2010), 407-423.
  7. On hyperelliptic modular curves over function fields, Archiv der Mathematik 92 (2009), 291-302.
  8. Genus formula for modular curves of D-elliptic sheaves, Archiv der Mathematik 92 (2009), 237-250.
  9. Modular varieties of D-elliptic sheaves and the Weil-Deligne bound, Journal für die reine und angewandte Mathematik 626 (2009), 115-134.
  10. On eigenvalues of p-adic curvature, Manuscripta Mathematica 127 (2008), 397-410.
  11. Modular curves of D-elliptic sheaves are asymptotically optimal, Mathematical Research Letters 15 (2008), 525-536.
  12. Analogue of the degree conjecture over function fields, Transactions of the American Mathematical Society 359 (2007), 3483-3503.
  13. Abelian subvarieties of Drinfeld Jacobians and congruences modulo the characteristic, Mathematische Annalen 337 (2007), 139-157.
  14. The number of rational points on Drinfeld modular varieties over finite fields, International Mathematics Research Notices Article ID 94356 (2006), 1-36.
  15. On the torsion of optimal elliptic curves over function fields, Mathematical Research Letters 13 (2006), 321-331.
  16. On the variation of Tate-Shafarevich groups of elliptic curves over hyperelliptic curves, Journal of Number Theory 115 (2005), 249-283.
  17. Rigid-analytic geometry and abelian varieties, Contemporary Mathematics 388 (2005), 145-160.
  18. Pesenti-Szpiro inequality for optimal elliptic curves, Journal of Number Theory 114 (2005), 361-393.
  19. On component groups of Jacobians of Drinfeld modular curves, Annales de l'Institut Fourier 54 (2004), 2163-2199.
  20. On the degree of modular parametrizations over function fields, Journal of Number Theory 97 (2002), 317-349.
  21. On coset coverings of solutions of homogeneous cubic equations over finite fields, Electronic Journal of Combinatorics 8 (2001), #R22 (joint with Ara Alexanian).
Preprints
  1. Non-archimedean uniformization and monodromy pairing, Contemporary Mathematics, to appear.
  2. Optimal quotients of Jacobians with toric reduction and component groups (joint with Joseph Rabinoff), submitted.
  3. Cuspidal divisor group, Shimura subgroup and rational torsion of Drinfeld modular Jacobian (joint with Fu-Tsun Wei), submitted.
  4. A global characterization of the Frobenius in division fields of rank 2 generic Drinfeld modules (joint with Alina Carmen Cojocaru).
Expository Notes (not intended for publication)
  1. Honda-Tate theorem for elliptic curves (2012).
  2. On Garland's vanishing theorem for SL(n) (2007).
  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).