Grothendieck-Riemann-Roch and its application to motives by Orlov

Some quantitative results in Diophantine approximation

Number of points over $\Bbb{F}_{q^{n}}$ for hyperelliptic curves defined over $\Bbb{F}_{q}$

Holonomic Rank Problem (II) and the Residue Formalism for Relative Cohomology.

The L^2 Volume of the Space of Holomorphic Maps from Closed Kahler Riemann Surfaces to Complex Projective Spaces via Vortex Equations.

Diophantine approximation in finite characteristic

Intersection theory IV: Intersection product and lci morphisms.

An algebraic Gromov-Witten type theory from D-strings

Special L-values and log-algebraicity on Drinfeld modules

On the holonomic rank conjecture

Some 3-variable Diophantine Equations and Arithmetic Dynamics

Special Values of Zeta-functions and Euler Characteristics

Intersection theory III: Construction of Intersection Products

The web of Calabi-Yau hypersurfaces in toric Fano 4-folds (II)

Tautological Systems and Poincare Residue Formula (II): Theory & Examples

Multiple polylogarithms as logarithms of certain t-modules

Magma and Computations in finite characteristic

Chern classes and Segre classes of bundles and cones.

Additive bases in groups

The web of Calabi-Yau hypersurfaces in toric Fano 4-folds (I)

Tautological Systems and Poincare Residue Formula (I): General Theory

Uniform boundedness of torsion of abelian varieties and Galois representations (joint work with Anna Cadoret)

Intersection theory I: Chow groups and rational equivalence

On a generalization of Artin's Conjecture to composite moduli

Deformations of Calabi-Yau hypersurfaces in toric varieties

Equidistribution of Polynomial Sequences in Function Fields

Holonomicity of GKZ-systems

Langlands program: review and outlook

Sparse Interpolation Problems