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.
  2. Optimal quotients of Mumford curves and component groups (joint with Joe Rabinoff).