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 and Humboldt Research Fellowship. 

       

Publications

  1. Modular varieties of D-elliptic sheaves and the Weil-Deligne bound, Journal für die reine und angewandte Mathematik, to appear.
  2. Modular curves of D-elliptic sheaves are asymptotically optimal, Mathematical Research Letters 15 (2008), 525-536. 
  3. Analogue of the degree conjecture over function fields, Transactions of the American Mathematical Society 359 (2007), 3483-3503.
  4. Abelian subvarieties of Drinfeld Jacobians and congruences modulo the characteristic, Mathematische Annalen 337 (2007), 139-157.
  5. The number of rational points on Drinfeld modular varieties over finite fields, International Mathematics Research Notices Article ID 94356 (2006), 1-36.
  6. On the torsion of optimal elliptic curves over function fields, Mathematical Research Letters 13 (2006), 321-331.
  7. On the variation of Tate-Shafarevich groups of elliptic curves over hyperelliptic curves, Journal of Number Theory 115 (2005), 249-283.
  8. Rigid-analytic geometry and abelian varieties, Contemporary Mathematics 388 (2005), 145-160.
  9. Pesenti-Szpiro inequality for optimal elliptic curves, Journal of Number Theory 114 (2005), 361-393.
  10. On component groups of Jacobians of Drinfeld modular curves, Annales de l'Institut Fourier 54 (2004), 2163-2199.
  11. On the degree of modular parametrizations over function fields, Journal of Number Theory 97 (2002), 317-349.
  12. 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. On eigenvalues of p-adic curvature, submitted for publication.