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