My research interests are primarily in the area of number theory. Specifically, I am interested in p-adic Galois representations and algebraic automorphic forms. I am currently working on a project that aims to giving an evidence towards mod-p Langlands program.
One formulation of a hypothetical mod-p local Langlands correspondence is the existence of an injection from the set of mod-p Galois representations to the set of mod-p admissible representations, which is compatible with global correspondence occurring in the mod-p cohomology of locally symmetric spaces. At present, the only known case of such a correspondence is GL_2(Q_p). For a given mod-p Galois representation, one can define a candidate of mod-p admissible representation for mod-p Langlands correspondence, via the global correspondence, and I am currently studying the structure of the candidate to see if it determines the given Galois representation.