My area of research is Arithmetic Algebraic Geometry, which is the common part of Number Theory, Algebra, and Geometry. I am very much interested in moduli spaces, group schemes, Lie algebras, formal group schemes, representation theory, cohomology theories, Galois theory, and the classification of projective, smooth, connected varieties. My research is focused on:
- Shimura varieties of Hodge type (which are moduli spaces of polarized abelian varieties endowed with Hodge cycles),
- arithmetic properties of abelian schemes,
- classification of
- representations of Lie algebras and reductive group schemes,
- crystalline cohomology of large classes of polarized varieties, and
- Galois representations associated to abelian varieties.
- PhD, Princeton University