We reprove the theorem of Feigin and Frenkel relating the center of the critical level enveloping algebra of the Kac-Moody algebra for a semisimple Lie algebra to opers (which are certain de Rham local systems with extra structure) for the Langlands dual group. Our proof incorporates a construction of Beilinson and Drinfeld relating the Feigin-Frenkel isomorphism to (more classical) Langlands d...

We describe a correspondence (or duality) between the q-characters of finite-dimensional representations of a quantum affine algebra and its Langlands dual in the spirit of [6, 4]. We prove this duality for the Kirillov–Reshetikhin modules. In the course of the proof we introduce and construct “interpolating (q, t)-characters” depending on two parameters which interpolate between the q-characte...

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...

We show that local-global compatibility (at split primes) away from p holds at all points of the p-adic eigenvariety of a definite n-variable unitary group. The novelty is we allow non-classical points, possibly non-étale over weight space. More precisely we interpolate the local Langlands correspondence for GLn across the eigenvariety by considering the fibers of its defining coherent sheaf. W...

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...