Related papers: On Langlands functoriality- reduction to the semis…
The geometric Langlands correspondence for function fields over finite fields has been proved by Frenkel, Gaitsgory, Vilonen. The aim of this article is to write translation for curves over the complex field and prove the correspondence in…
We construct the Langlands correspondence for connected reductive groups over finite fields, which we call the finite Langlands correspondence. We discuss also its relation with the categorical local Langlands correspondence.
Langlands' functoriality principle predicts deep relations between the local and automorphic spectra of different reductive groups. This has been generalized by the relative Langlands program to include spherical varieties, among which…
We show that, over a nonarchimedean local field, the rigid refined local Langlands correspondence and associated endoscopic character identities for connected reductive $G$ follow if one only has them for all such $G$ with connected center.…
The goal of this paper is to give a simple proof of Deligne's conjecture (proven by Fujiwara) and to generalize it to the situation appearing in our joint project with David Kazhdan on the global Langlands correspondence over function…
We extend the Langlands program in various subprograms with certain different generalizations: (1) Mixed-parity functorial perturbation of the usual Langlands program after Fargues-Scholze in all characteristics; (2) Robba-Frobenius…
There has been a recent coming together of the Converse Theorem for $\gln$ and the Langlands-Shahidi method of controlling the analytic properties of automorphic $L$-functions which has allowed us to establish a number of new cases of…
This paper is devoted to heuristic aspects of the so-called idempotent calculus. There is a correspondence between important, useful and interesting constructions and results over the field of real (or complex) numbers and similar…
We argue that Lagrangian correspondences are the correct framework to study functoriality of virtual fundamental classes arising from a $-2$-symplectic derived structure.
We construct the local Langlands correspondence of essentially unipotent supercuspidal representations under the framework of rigid inner forms and prove a certaion functoriality and compatibilities. This result is stronger than the…
In the Proceedings of the AMS Boulder conference in 1965 Langlands states a combinatorial lemma involving families of characteristic functions attached to ordered partitions of an obtuse basis in a finite dimensional euclidean vector space.…
The Langlands functoriality conjecture envisaged in the bisemialgebra framework is proved to correspond to the nonorthogonal completely reducible cuspidal representations of the bilinear algebraic semigroups.
The Langlands correspondence for complex curves is traditionally formulated in terms of sheaves rather than functions. Recently, Langlands asked whether it is possible to construct a function-theoretic version. In this paper we use the…
We develop a stochastic calculus that makes it easy to capture a variety of predictable transformations of semimartingales such as changes of variables, stochastic integrals, and their compositions. The framework offers a unified treatment…
The global Jacquet--Langlands correspondence is an instance of Langlands functoriality, namely the expected lifting of the irreducible automorphic representations of an inner form of the general linear group to the split form via the…
There are two versions of endoscopic transfer factors to accommodate the different versions, classical or renormalized, of the local Langlands correspondence. An examination of the structure of these complex-valued factors shows that the…
We establish the Langlands-Shahidi method over a global field of characteristic p. We then focus on the unitary groups and prove global and local Langlands functoriality to general linear groups for generic representations. Main…
This paper performs the following steps toward the proof of GLC in the de Rham setting: (i) We deduce GLC for G=GL_n; (ii) We prove that the Langlands functor L_G constructed in [GLC1], when restricted to the cuspidal category, is…
Using quilted Floer cohomology and relative quilt invariants, we define a composition functor for categories of Lagrangian correspondences in monotone and exact symplectic Floer theory. We show that this functor agrees with geometric…
Logical relations built on top of an operational semantics are one of the most successful proof methods in programming language semantics. In recent years, more and more expressive notions of operationally-based logical relations have been…