I am interested in algebraic number theory, especially in the theory of Drinfeld modular varieties and related topics.
        My research is currently supported by NSF grant DMS-0801208. 
Curriculum Vitae. 

Publications

  1. On generators of arithmetic groups over function fields, International Journal of Number Theory, to appear.
  2. Local diophantine properties of modular curves of D-elliptic sheaves, Journal für die reine und angewandte Mathematik, to appear.
  3. On Jacquet-Langlands isogeny over function fields, Journal of Number Theory 131 (2011), 1149-1175.
  4. On finite arithmetic simplicial complexes, Proceedings of the American Mathematical Society 139 (2011), 111-124.
  5. Endomorphisms of exceptional D-elliptic sheaves, Mathematische Zeitschrift 266 (2010), 407-423. 
  6. On hyperelliptic modular curves over function fields, Archiv der Mathematik 92 (2009), 291-302. 
  7. Genus formula for modular curves of D-elliptic sheaves, Archiv der Mathematik 92 (2009), 237-250. 
  8. Modular varieties of D-elliptic sheaves and the Weil-Deligne bound, Journal für die reine und angewandte Mathematik 626 (2009), 115-134.
  9. On eigenvalues of p-adic curvature, Manuscripta Mathematica 127 (2008), 397-410.
  10. Modular curves of D-elliptic sheaves are asymptotically optimal, Mathematical Research Letters 15 (2008), 525-536. 
  11. Analogue of the degree conjecture over function fields, Transactions of the American Mathematical Society 359 (2007), 3483-3503.
  12. Abelian subvarieties of Drinfeld Jacobians and congruences modulo the characteristic, Mathematische Annalen 337 (2007), 139-157.
  13. The number of rational points on Drinfeld modular varieties over finite fields, International Mathematics Research Notices Article ID 94356 (2006), 1-36.
  14. On the torsion of optimal elliptic curves over function fields, Mathematical Research Letters 13 (2006), 321-331.
  15. On the variation of Tate-Shafarevich groups of elliptic curves over hyperelliptic curves, Journal of Number Theory 115 (2005), 249-283.
  16. Rigid-analytic geometry and abelian varieties, Contemporary Mathematics 388 (2005), 145-160.
  17. Pesenti-Szpiro inequality for optimal elliptic curves, Journal of Number Theory 114 (2005), 361-393.
  18. On component groups of Jacobians of Drinfeld modular curves, Annales de l'Institut Fourier 54 (2004), 2163-2199.
  19. On the degree of modular parametrizations over function fields, Journal of Number Theory 97 (2002), 317-349.
  20. On coset coverings of solutions of homogeneous cubic equations over finite fields, Electronic Journal of Combinatorics 8 (2001), #R22 (Joint paper with A. Alexanian).

Preprints

  1. D-elliptic sheaves and odd Jacobians, preprint.