Let F be a non-Archimedean local field of characteristic 0 and G be an inner form of the general linear group G = GLn over F . We show that the rectifying character appearing in the essentially tame Jacquet-Langlands correspondence of Bushnell and Henniart for G and G can be factorized into a product of some special characters, called zeta-data in this paper, in the theory of endoscopy of Langl...

The transfer factors for standard endoscopy involve, among other things, the Langlands-Shelstad splitting invariant. This note introduces a twisted version of that splitting invariant. The twisted splitting invariant is then used to define a better twisted factor ∆I . In addition we correct a sign error in the definition of twisted transfers. There are two ways to correct the sign error. One wa...

The Langlands Program relates Galois representations and automorphic representations of reductive algebraic groups. The trace formula is a powerful tool in the study of this connection and the Langlands Functoriality Conjecture. After giving an introduction to the Langlands Program and its geometric version, which applies to curves over finite fields and over the complex field, I give a survey ...

Using theta correspondence, we obtain a classification of irreducible representations an arbitrary even orthogonal group (i.e. the local Langlands correspondence) by deducing it from correspondence for symplectic groups due to Arthur. Moreover,we show that our classifications coincide with established Arthur and formulated precisely Atobe-Gan quasi-split groups.

My research interest lies in the area of arithmetic geometry related to Langlands correspondence, where the theory of automorphic forms and algebraic geometry intersect. It is one of the most interesting and actively studied subject of algebraic number theory, whose origin goes back to the theory of complex multiplication. My research is currently focused on the local aspect of this theory, nam...

For certain mod p Galois representations ρ̄, arising from modular forms on definite unitary groups in two variables, we express the ρ̄-part of completed cohomology Ĥ ρ̄ (away from Σ = Σp ∪Σ0) as a tensor product Πp⊗ΠΣ0 . Here Πp is attached to the universal deformation ρ via the p-adic local Langlands correspondence for GL2(Qp), and ΠΣ0 is given by the local Langlands correspondence in families, o...